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Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent

Stegliński Robert

Opuscula Mathematica

2022

Vol. 42, no. 5

751--761

Using the Dual Fountain Theorem we obtain some existence of infinitely many solutions for local and nonlocal elliptic equations with variable exponent. Our results correct some of the errors that have appeared recently in the literature.

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.