Anisotropic nonlinear Neumann problems

By Leszek Gasinski, Nikolaos S. Papageorgiou. 2011

78 citations recorded by the source corpus.

We consider nonlinear Neumann problems driven by the p(z)-Laplacian differential operator and with a p-superlinear reaction which does not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). In the process, we also prove two results of independent interest. The first is about the L∞-boundedness of the weak solutions. The second relates W1,p(z) and C1 local minimizers.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d26851a4beb807129f85e9d51246857818f373c4

Citations in the corpus

• Moser iteration applied to elliptic equations with critical growth on the boundary (2018, unknown): “Finally, we mention some works concerning boundedness and regularity results of weak solutions to quasilinear equations of the form (1.1) that have subcritical growth, see, for example, Fan-Zhao [3], Gasiński-Papageorgiou [5], [7, pp. 737– 738], Hu-Papageorgiou [9], Lê [10], Motreanu-Motreanu-Papa”