Semilinear Robin problems resonant at both zero and infinity

References

[1] S. Aizicovici, N. S. Papageorgiou and V. Staicu, Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints, Mem. Amer. Math. Soc. 915 (2008), 1–70. 10.1090/memo/0915Search in Google Scholar

[2] G. Barletta and N. S. Papageorgiou, Periodic problems with double resonance, NoDEA Nonlinear Differential Equations Appl. 19 (2012), 303–328. 10.1007/s00030-011-0130-5Search in Google Scholar

[3] S. Cingolani and M. Degiovanni, Nontrivial solutions for p-Laplace equations with right-hand side having p-linear growth at infinity, Comm. Partial Differential Equations 30 (2005), 1191–1203. 10.1080/03605300500257594Search in Google Scholar

[4] J. N. Corvellec and A. Hantoute, Homotopical stability of isolated critical points of continuous functionals, Set-Valued Var. Anal. 10 (2002), 143–164. 10.1023/A:1016544301594Search in Google Scholar

[5] M. Degiovanni and S. Lancelotti, Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), 907–919. 10.1016/j.anihpc.2006.06.007Search in Google Scholar

[6] F. O. de Paiva, Multiple solutions for asymptotically linear resonant elliptic problems, Topol. Methods Nonlinear Anal. 21 (2003), 227–247. 10.12775/TMNA.2003.014Search in Google Scholar

[7] E. R. Fadell and P. Rabinowitz, Generalized cohomological index theories for Lie group actions with applications to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139–174. 10.1007/BF01390270Search in Google Scholar

[8] L. Gasinski and N. S. Papageorgiou, Nonlinear Analysis, Chapman & Hall/CRC, Boca Raton, 2006. 10.1201/9781420035049Search in Google Scholar

[9] L. Gasinski and N. S. Papageorgiou, Neumann problems resonant at zero and infinity, Ann. Mat. Pura Appl. (4) 191 (2012), 395–430. 10.1007/s10231-011-0188-zSearch in Google Scholar

[10] E. M. Landesman, S. Robinson and A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal. 24 (1995), 1049–1059. 10.1016/0362-546X(94)00107-SSearch in Google Scholar

[11] C. Li, The existence of infinitely many solutions of a class of nonlinear elliptic equations with Neumann boundary condition for both resonance and oscillation problems, Nonlinear Anal. 54 (2003), 431–443. 10.1016/S0362-546X(03)00100-7Search in Google Scholar

[12] C. Li and S. Li, Multiple solutions and sign-changing solutions of a class of nonlinear elliptic equations with Neumann boundary condition, J. Math. Anal. Appl. 298 (2004), 14–32. 10.1016/j.jmaa.2004.01.017Search in Google Scholar

[13] S. Li and M. Willem, Multiple solutions for asymptotically linear boundary value problems in which the nonlinearity crosses at least one eigenvalue, NoDEA Nonlinear Differential Equations Appl. 5 (1998), 479–490. 10.1007/s000300050058Search in Google Scholar

[14] Z. Liang and J. Su, Multiple solutions for semilinear elliptic boundary value problems with double resonance, J. Math. Anal. Appl. 354 (2009), 147–158. 10.1016/j.jmaa.2008.12.053Search in Google Scholar

[15] D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Topological and Variational Methods with Applications to Boundary Value Problems, Springer, New York, 2014. 10.1007/978-1-4614-9323-5Search in Google Scholar

[16] R. Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966), 1–16. 10.1016/0040-9383(66)90002-4Search in Google Scholar

[17] N. S. Papageorgiou and V. D. Rădulescu, Multiple solutions with precise sign information for nonlinear parametric Robin problems, J. Differential Equations 256 (2014), 2449–2479. 10.1016/j.jde.2014.01.010Search in Google Scholar

[18] N. S. Papageorgiou and V. D. Rădulescu, Multiplicity of solutions for resonant Neumann problems with an indefinite and unbounded potential, Trans. Amer. Math. Soc. 367 (2015), 8723–8756. 10.1090/S0002-9947-2014-06518-5Search in Google Scholar

[19] N. S. Papageorgiou and V. D. Rădulescu, Resonant (p,2)-equations with asymmetric reaction, Anal. Appl. (Singap.) 13 (2015), 481–506. 10.1142/S0219530514500134Search in Google Scholar

[20] A. Quin, Existence of infinitely many solutions for a superlinear Neumann boundary value problem, Bound. Value Probl. 2005 (2005), 329–335. 10.1155/BVP.2005.329Search in Google Scholar

[21] J. Su, Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues, Nonlinear Anal. 44 (2001), 311–321. 10.1016/S0362-546X(00)00221-2Search in Google Scholar

[22] X.-J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations 93 (1991), 283–310. 10.1016/0022-0396(91)90014-ZSearch in Google Scholar