Startseite Mathematik Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential

  • Daniel Paşca EMAIL logo
Veröffentlicht/Copyright: 28. April 2017
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 67 Heft 2

Abstract

A result for the existence of homoclinic orbits is obtained for (q, p)-Laplacian systems.

MSC 2010: Primary 37J45; 58E05; 34C37; 70H05
Keywords: Homoclinic solutions; (q, p)-Laplacian systems; coercive potential

(Communicated by Michal Fečkan)

References

[1] Ambrosetti, A.—Coti Zelati, V.: Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova 89 (1993), 177—194.Suche in Google Scholar

[2] Carrlão, P. C.—Miyagaki, O. H.: Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems, J. Math. Anal. Appl. 230 (1999), 157—172.10.1006/jmaa.1998.6184Suche in Google Scholar

[3] Coti Zelati, V.—Rabinowitz, P. H.: Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991), 693—727.10.1090/S0894-0347-1991-1119200-3Suche in Google Scholar

[4] Crînganu, J.—Paşca, D.: Existence of periodic solutions for nonautonomous second order differential systems with (p1,p2)-Laplacian using the duality mappings, Ann. Univ. Buchar. Math. Ser. 2 (2011), 139—155.Suche in Google Scholar

[5] Ding, Y.—Li, S. J.: Homoclinic orbits for first order Hamiltonian systems, J. Math. Anal. Appl. 189 (1995), 585-601.10.1006/jmaa.1995.1037Suche in Google Scholar

[6] Izydorek, M.—Janczewska, J.: Homoclinic solutions for a class of the second order Hamiltonian systems, J. Differential Equations 219 (2005), 375-389.10.1016/j.jde.2005.06.029Suche in Google Scholar

[7] Izydorek, M.—Janczewska, J.: Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential, J. Math. Anal. Appl. 335 (2007), 1119-1127.10.1016/j.jmaa.2007.02.038Suche in Google Scholar

[8] Lu, S.: Homoclinic solutions for a nonlinear second order differential system with p-Laplacian operator, Nonlinear Anal. Real World Appl. 12 (2011), 525-534.10.1016/j.nonrwa.2010.06.037Suche in Google Scholar

[9] Lu, S.—Lu, M.: Homoclinic solutions for a second-order p-Laplacian functional differential system with local condition, Adv. Differ. Equ. (2014), 2014: 24410.1186/1687-1847-2014-244Suche in Google Scholar

[10] Ma, J.—Tang, Ch.-L.: Periodic solutions for some nonautonomous second-order systems , J. Math. Anal. Appl. 275 (2002), 482-494.10.1016/S0022-247X(02)00636-4Suche in Google Scholar

[11] Mawhin, M.—Willem, J.: Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin/New York, 1989.10.1007/978-1-4757-2061-7Suche in Google Scholar

[12] Paşca, D.: Periodic solutions for second order differential inclusions, Comm. Appl. Nonlinear Anal. 6 (1999), 91-98Suche in Google Scholar

[13] Paşca, D.: Periodic solutions for second order differential inclusions with sublinear nonlinearity, Panamer. Math. J. 10 (2000), 35-45.Suche in Google Scholar

[14] Paşca, D.: Periodic solutions of a class of non-autonomous second order differential inclusions systems, Abstr. Appl. Anal. 6 (2001), 151—161.10.1155/S1085337501000525Suche in Google Scholar

[15] Paşca, D.: Periodic solutions of second-order differential inclusions systems with p-Laplacian, J. Math. Anal. Appl. 325 (2007), 90-100.10.1016/j.jmaa.2006.01.061Suche in Google Scholar

[16] Paşca, D.—Tang, Ch-L.: Subharmonic solutions for nonautonomous sublinear second order differential inclusions systems with p-Laplacian, Nonlinear Anal. 69 (2008), 1083-1090.10.1016/j.na.2007.06.019Suche in Google Scholar

[17] Paşca, D.: Periodic solutions for nonautonomous second order differential inclusions systems with p-Laplacian, Comm. Appl. Nonlinear Anal. 16 (2009), 13-23.Suche in Google Scholar

[18] Paşca, D.—Tang, Ch.-L.: Some existence results on periodic solutions of nonautonomous second order differential systems with (q,p)-Laplacian, Appl. Math. Lett. 23 (2010), 246-251.10.1016/j.aml.2009.10.005Suche in Google Scholar

[19] Paşca, D.: Periodic solutions of a class of nonautonomous second order differential systems with (q,p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 841-850.10.36045/bbms/1292334059Suche in Google Scholar

[20] Paşca, D.—Tang, Ch.-L.: Some existence results on periodic solutions of ordinary (q,p)-Laplacian systems, J. Appl. Math. Inform. 29 (2011), 38-48.Suche in Google Scholar

[21] Paşca, D.: Periodic solutions of second-order differential inclusions systems with (q,p)-Laplacian, Anal. Appl. 9 (2011), 201-223.10.1142/S0219530511001819Suche in Google Scholar

[22] Paşca, D.—Tang, Ch.-L.: New existence results on periodic solutions of nonautonomous second order differential systems with (q,p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 19 (2012), 19-27.10.36045/bbms/1331153405Suche in Google Scholar

[23] Paşca, D.—Wang, ZH.: New existence results on periodic solutions of nonautonomous second order Hamiltonian systems with (q,p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 155-166.10.36045/bbms/1366306721Suche in Google Scholar

[24] Paşca, D.—Tang, Ch.-L.: Periodic solutions of non-autonomous second order systems with (q(t),p(t))Laplacian, Math. Slovaca 64 (2014), 913-930.10.2478/s12175-014-0248-0Suche in Google Scholar

[25] Rabinowitz, P. H.: On subharmonic solutions of Hamiltonian systems, Commun. Pure Appl. Math. 33 (1980), 609-633.10.1002/cpa.3160330504Suche in Google Scholar

[26] Rabinowitz, P. H.: Periodic and heteroclinic orbits for a periodic Hamiltonian systems, Ann. Inst. H. PoincaréAnal. Non Linéaire 6 (1989), 331-346.10.21236/ADA204078Suche in Google Scholar

[27] Rabinowitz, P. H.: Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A 114 (1990), 33-38.10.21236/ADA210562Suche in Google Scholar

[28] Rabinowitz, P.—Tanaka, H. K.: Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206 (1991), 473-499.10.1007/BF02571356Suche in Google Scholar

[29] Séré, E.: Existence of infinitely many homoclinic orbit in Hamiltonian systems, Math. Z. 209 (1992), 27-42.10.1007/BF02570817Suche in Google Scholar

[30] Szulkin, A.—Zou, W.: Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal. 187 (2001), 25-41.10.1006/jfan.2001.3798Suche in Google Scholar

[31] Tang, X. H.— Xiao, L.: Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential, Nonlinear Anal. 71 (2009), 1124-1132.10.1016/j.na.2008.11.027Suche in Google Scholar

[32] Tang, X. H.— Xiao, L.: Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential, J. Math. Anal. Appl. 351 (2009), 585-594.10.1016/j.jmaa.2008.10.038Suche in Google Scholar

[33] Tang, Ch.-L.: Periodic solutions of nonautonomous second-order systems with ϒ -quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), 671-675. 10.1006/jmaa.1995.1044Suche in Google Scholar

[34] Tang, Ch.-L.: Periodic solutions of nonautonomous second order systems, J. Math. Anal. Appl. 202 (1996), 465-469.10.1006/jmaa.1996.0327Suche in Google Scholar

[35] Tang, Ch.-L.: Periodic solutions for nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), 3263-3270.10.1090/S0002-9939-98-04706-6Suche in Google Scholar

[36] Tang, Ch.-L.: Existence and multiplicity of periodic solutions of nonautonomous second order systems, Nonlinear Anal. 32 (1998), 299-304.10.1016/S0362-546X(97)00493-8Suche in Google Scholar

[37] Tang, Ch.-L.—Wu, X.-P.: Periodic solutions for second order systems with not uniformly coercive potential, J. Math. Anal. Appl. 259 (2001), 386-397.10.1006/jmaa.2000.7401Suche in Google Scholar

[38] Tang, Ch.-L.—Wu, X.-P.: Notes on periodic solutions of subquadratic second order systems, J. Math. Anal. Appl. 285 (2003), 8-16.10.1016/S0022-247X(02)00417-1Suche in Google Scholar

[39] Tang, Ch.-L.—Wu, X.-P.: Subharmonic solutions for nonautonomous second order Hamiltonian systems, J. Math. Anal. Appl. 304 (2005), 383-393.10.1016/j.jmaa.2004.09.032Suche in Google Scholar

[40] Tang, Ch.-L.—Wu, X.-P.: Some critical point theorems and their applications to periodic solution for second order Hamiltonian systems, J. Diff. Eqs. 248 (2010), 660-692.10.1016/j.jde.2009.11.007Suche in Google Scholar

[41] Tian, Y.—Ge, W.: Periodic solutions of non-autonomous second-order systems with a p-Laplacian, Nonlinear Anal. 66 (2007), 192-203.10.1016/j.na.2005.11.020Suche in Google Scholar

[42] Wu, X.-P.: Periodic solutions for nonautonomous second-order systems with bounded nonlinearity, J. Math. Anal. Appl.230 (1999), 135-141.10.1006/jmaa.1998.6181Suche in Google Scholar

[43] Wu, X.-P.—Tang, Ch.-L.: Periodic solutions of a class of non-autonomous second-order systems, J. Math. Anal. Appl. 236 (1999), 227-235.10.1006/jmaa.1999.6408Suche in Google Scholar

[44] Wu, X.-P.—Tang, Ch.-L.: Periodic solutions of nonautonomous second-order Hamiltonian systems with even-typed potentials, Nonlinear Anal. 55 (2003), 759-769.10.1016/j.na.2003.08.009Suche in Google Scholar

[45] Xu, B.—Tang, Ch.-L.: Some existence results on periodic solutions of ordinary p-Laplacian systems, J. Math. Anal. Appl. 333 (2007), 1228-1236.10.1016/j.jmaa.2006.11.051Suche in Google Scholar

[46] Zhao, F.—Wu, X.: Saddle point reduction method for some non-autonomous second order systems, J. Math. Anal. Appl. 291 (2004), 653-665.10.1016/j.jmaa.2003.11.019Suche in Google Scholar

Received: 2014-11-19
Accepted: 2015-3-15
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  2. 10.1515/ms-2015-0200
  4. Zero-divisor graphs of lower dismantlable lattices I
  6. Some results on the intersection graph of submodules of a module
  8. Class number parities of compositum of quadratic function fields
  10. Examples of beurling prime systems
  12. Connection between multiplication theorem for Bernoulli polynomials and first factor hp−
  14. On permutational invariance of the metric discrepancy results
  16. Evaluation of sums containing triple aerated generalized Fibonomial coefficients
  18. Linear algebraic proof of Wigner theorem and its consequences
  20. A note on groups with finite conjugacy classes of subnormal subgroups
  22. Groups with the same complex group algebras as some extensions of psl(2, pn)
  24. Klee-Phelps convex groupoids
  26. On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
  28. Weak interpolation for the lipschitz class
  30. Generalized Padé approximants for plane condenser and distribution of points
  32. Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
  34. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
  36. Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
  38. Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
  40. On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
  42. Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
  44. Semi-equivelar maps on the torus and the Klein bottle with few vertices
  46. A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
https://doi.org/10.1515/ms-2016-0285
Schlagwörter für diesen Artikel
Homoclinic solutions; (q, p)-Laplacian systems; coercive potential

Artikel in diesem Heft

  2. 10.1515/ms-2015-0200
  4. Zero-divisor graphs of lower dismantlable lattices I
  6. Some results on the intersection graph of submodules of a module
  8. Class number parities of compositum of quadratic function fields
  10. Examples of beurling prime systems
  12. Connection between multiplication theorem for Bernoulli polynomials and first factor hp−
  14. On permutational invariance of the metric discrepancy results
  16. Evaluation of sums containing triple aerated generalized Fibonomial coefficients
  18. Linear algebraic proof of Wigner theorem and its consequences
  20. A note on groups with finite conjugacy classes of subnormal subgroups
  22. Groups with the same complex group algebras as some extensions of psl(2, pn)
  24. Klee-Phelps convex groupoids
  26. On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
  28. Weak interpolation for the lipschitz class
  30. Generalized Padé approximants for plane condenser and distribution of points
  32. Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
  34. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
  36. Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
  38. Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
  40. On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
  42. Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
  44. Semi-equivelar maps on the torus and the Klein bottle with few vertices
  46. A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2016-0285/html
Button zum nach oben scrollen