Elliptic equations with indefinite and unbounded potential and a nonlinear concave boundary condition

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. 196 (2008) 70. ISI, Google Scholar
• 2. S. Aizicovici, N. S. Papageorgiou and V. Staicu, On a $p$-superlinear Neumann $p$-Laplacian equation, Topol. Methods Nonlinear Anal. 34 (2009) 111–130. Crossref, ISI, Google Scholar
• 3. A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994) 519–543. Crossref, ISI, Google Scholar
• 4. A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349–381. Crossref, Google Scholar
• 5. G. Barletta, R. Livrea and N. S. Papageorgiou, A nonlinear eigenvalue problem for the periodic scalar $p$-Laplacian, Comm. Pure. Appl. Anal. 13 (2014) 1075–1086. Crossref, ISI, Google Scholar
• 6. A. Castro, J. Cossio and C. Vélez, Existence and qualitative properties of solutions for nonlinear Dirichlet problems, Discrete Contin. Dyn. Syst. 33 (2013) 123–140. Crossref, ISI, Google Scholar
• 7. M. Filippakis, A. Kristaly and N. S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation, Discrete Contin. Dyn. Syst. 24 (2009) 405–440. Crossref, ISI, Google Scholar
• 8. M. Furtado and R. Ruviaro, Multiple solutions for a semilinear problem with combined terms and nonlinear boundary conditions, Nonlinear Anal. 74 (2011) 4820–4830. Crossref, ISI, Google Scholar
• 9. J. Garcia Azorero, I. Peral and J. Rossi, A convex-concave problem with a nonlinear boundary condition, J. Differential Equations 198 (2004) 91–128. Crossref, ISI, Google Scholar
• 10. L. Gasinski and N. S. Papageorgiou, Nonlinear Analysis (Chapman & Hall/CRC, Boca Raton, 2006). Google Scholar
• 11. L. Gasinski and N. S. Papageorgiou, Dirichlet $(p,q)$-equations at resonance, Discrete Contin. Dyn. Syst. 34 (2014) 2037–2060. Crossref, ISI, Google Scholar
• 12. S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis Volume I: Theory (Kluwer Academic Publishers, Dordrecht, 1997). Crossref, Google Scholar
• 13. S. Kyritsi and N. S. Papageorgiou, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term, Discrete Cont. Dyn. Syst. 33 (2013) 2469–2494. Crossref, ISI, Google Scholar
• 14. S. Marano and N. S. Papageorgiou, Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter, Comm. Pure Appl. Anal. 12 (2013) 815–829. Crossref, ISI, Google Scholar
• 15. V. Moroz, Solutions of superlinear at zero elliptic equations via Morse theory, Topol. Methods Nonlinear Anal. 10 (1997) 387–397. Crossref, Google Scholar
• 16. D. Motreanu, V. Motreanu and N. S. Papageorgiou, Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (Springer, New York, 2014). Crossref, Google Scholar
• 17. R. Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 115–132. Crossref, Google Scholar
• 18. N. S. Papageorgiou and V. D. Radulescu, Multiple solutions with precise sign information for parametric Robin problems, J. Differential Equations 256 (2014) 2449–2479. Crossref, ISI, Google Scholar
• 19. N. S. Papageorgiou and V. D. Radulescu, Neumann problems with indefinite and unbounded potential and concave terms, Proc. Amer. Math. Soc. 143 (2015) 4803–4816. Crossref, ISI, Google Scholar
• 20. X. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations 93 (1991) 283–310. Crossref, ISI, Google Scholar
• 21. E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B (Springer, New York, 1990). Google Scholar