Superlinear Robin problems with indefinite linear part
DOI:
https://doi.org/10.5604/01.3001.0012.0898Keywords:
indefinite and unbounded potential, superlinear reaction, almost critical growth, regularity theory, local linking, infinitely many solutionsAbstract
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.
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