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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.