System of nonlocal resonant boundary value problems involving p-Laplacian
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Katarzyna Szymańska-Dębowska
Abstract
Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem
where the function ϕ : ℝn → ℝn is given by ϕ (s) = (φp1(s1), …, φpn(sn)), s ∈ ℝn, pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝn × ℝn → ℝn is continuous and g : [0,1] → ℝn is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.
Communicated by Michal Fečkan
References
[1] Bai, C.—Fang, J.: Existence of positive solutions for three-point boundary value problems at resonance, J. Math. Anal. Appl. 291 (2004), 538–549.10.1016/j.jmaa.2003.11.014Search in Google Scholar
[2] Cremins, C. T.: A fixed-point index and existence theorems for semilinear equations in cones, Nonlinear Anal. 46 (2001), 789–806.10.1016/S0362-546X(00)00144-9Search in Google Scholar
[3] Eloe, P. W.—Khan, R. A.—Asif, N.: Positive solutions for a system of singular second order nonlocal boundary value problems, J. Korean Math. Soc. 47 (2010), 985–1000.10.4134/JKMS.2010.47.5.985Search in Google Scholar
[4] Feng, W.: On an M-point boundary value problem, Nonlinear Anal. 30 (1997), 5369–5374.10.1016/S0362-546X(97)00360-XSearch in Google Scholar
[5] Franco, D.—Infante, G.—Zima, M.: Second order nonlocal boundary value problems at resonance, Math. Nachr. 284 (2011), 875–884.10.1002/mana.200810841Search in Google Scholar
[6] Ge, W.—Ren, J.: An extension of Mawhin’s continuation theorem and its application to boundary value problems with a p-Laplacian, Nonlinear Anal. 58 (2004), 477–488.10.1016/j.na.2004.01.007Search in Google Scholar
[7] Gupta, C. P.: A generalized multi-point boundary value problem for second order ordinary differential equations, Appl. Math. Comput. 89 (1998), 133–146.10.1016/S0096-3003(97)81653-0Search in Google Scholar
[8] Han, X.: Positive solutions for a three-point boundary value problem at resonance, J. Math. Anal. Appl. 336 (2007), 556–568.10.1016/j.jmaa.2007.02.069Search in Google Scholar
[9] Hartman, P.: On boundary value problems for systems of ordinary, nonlinear, second order differential equations, Trans. Amer. Math. Soc. 96 (1960), 493–509.10.1090/S0002-9947-1960-0124553-5Search in Google Scholar
[10] Infante, G.—Webb, J. R. L.: Three-point boundary value problems with solutions that change sign, J. Integral Equations Appl. 15 (2003), 37–57.10.1216/jiea/1181074944Search in Google Scholar
[11] Infante, G.—Webb, J. R. L.: Positive solutions of some nonlocal boundary value problems, Abstr. Appl. Anal. 18 (2003), 1047–1060.10.1155/S1085337503301034Search in Google Scholar
[12] Lipowski, A.—Przeradzki, B.—Szymańska-Dębowska, K.: Periodic solutions to differential equations with a generalized p-Laplacian, Discrete Contin. Dyn. Syst. Ser. B 19(8) (2014), 2593–2601.10.3934/dcdsb.2014.19.2593Search in Google Scholar
[13] Manásevich, R.—Mawhin, J.: Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations 145 (1998), 367–393.10.1006/jdeq.1998.3425Search in Google Scholar
[14] Picone, M.: Su un problema al contorno nelle equazioni differenziali lineari ordinarie del secondo ordine, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (1908), 1–95.Search in Google Scholar
[15] Webb, J. R. L.—Infante, G.: Positive solutions of nonlocal boundary value problems: a unified approach, J. London Math. Soc. (2) 74 (2006), 673–693.10.1112/S0024610706023179Search in Google Scholar
[16] Webb, J. R. L.—Infante, G.: Positive solutions of nonlocal boundary value problems involving integral conditions, NoDEA Nonlinear Differential Equations Appl. 15 (2008), 45–67.10.1007/s00030-007-4067-7Search in Google Scholar
[17] Webb, J. R. L.—Zima, M.: Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems, Nonlinear Anal. 71 (2009), 1369–1378.10.1016/j.na.2008.12.010Search in Google Scholar
[18] Whyburn, W. M.: Differential equations with general boundary conditions, Bull. Amer. Math. Soc. 48 (1942), 692–704.10.1090/S0002-9904-1942-07760-3Search in Google Scholar
[19] Zhang, X.—Feng, M.—Ge, W.: Existence result of second-order differential equations with integral boundary conditions at resonance, J. Math. Anal. Appl. 353 (2009), 311–319.10.1016/j.jmaa.2008.11.082Search in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
- Distance functions on the sets of ordinary elliptic curves in short Weierstrass form over finite fields of characteristic three
- The drazin inverse of the sum of two matrices
- Refinements of the majorization-type inequalities via green and fink identities and related results
- Characterizations and properties of graphs of Baire functions
- Some improvements of the young mean inequality and its reverse
- On characteristic of bounded analytic functions involving hyperbolic derivative
- A uniqueness problem for entire functions related to Brück’s conjecture
- System of nonlocal resonant boundary value problems involving p-Laplacian
- Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
- Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces
- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
- On generalized 4-th root metrics of isotropic scalar curvature
- Compactifications from generators and relations
- Diophantine quadruples with values in k-generalized Fibonacci numbers
