Nonlinear Nonhomogeneous Robin Problems with Superlinear Reaction Term

By Nikolaos S. Papageorgiou, Vicentiu D. Rădulescu. 2016

147 citations recorded by the source corpus.

Abstract We consider a nonlinear Robin problem driven by a nonlinear, nonhomogeneous differential operator, and with a Carathéodory reaction term which is (p-1)${{(p-1)}}$-superlinear near ±∞${\pm\infty}$ without satisfying the Ambrosetti–Rabinowitz condition and which does not have a standard subcritical polynomial growth. Using a combination of variational methods and Morse theoretic techniques, we prove a multiplicity theorem producing three nontrivial solutions (two of which have constant sign). In the process we establish some useful facts about the boundedness of the weak solutions of critical equations and the relation of Sobolev and Hölder local minimizers for functionals with a critical perturbation term.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e1383398f8b037a53c13e833adff0667946c4566

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Moser iteration applied to elliptic equations with critical growth on the boundary (2018, background): “Note that our setting is more general than those in [14] since we have weaker conditions on a and f0 and our boundary term is able to have critical growth.”
Existence and multiplicity of solutions for double‐phase Robin problems (2020, background): “We refer to the very recent works of Bahrouni, Rădulescu and Repovš [1, 2] and the references therein.”
Positive solutions for nonlinear Neumann problems with singular terms and convection (2020, background): “By (13) and Proposition 7 of Papageorgiou & Rădulescu [18], we have uǫ ∈ L (Ω).”