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Superlinear Robin problems with indefinite linear part

Gasiński L., Papageorgiou N. S.

Science, Technology and Innovation

2018

Vol. 2, no. 1

74--94

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a superlinear reaction term which need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools we prove two theorems. An existence theorem producing a nontrivial smooth solution and a multiplicity theorem producing a whole unbounded sequence of nontrivial smooth solutions.

Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

Gasiński L., Papageorgiou N. S.

Schedae Informaticae

2012

Vol. 21

27--40

We consider a nonlinear Neumann elliptic equation driven by the p-Laplacian and a Caratheodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.