Existence of five nonzero solutions with exact sign for A p-laplacian equation

By Michael E. Filippakis, Alexandru Kristály, Nikolaos S. Papageorgiou. 2009

56 citations recorded by the source corpus.

We consider nonlinear elliptic problems driven by the $p$-Laplacian with a nonsmooth potential depending on a parameter $\lambda\ >\ 0$. The main result guarantees the existence of two positive, two negative and a nodal (sign-changing) solution for the studied problem whenever $\lambda\ >\ 0$ belongs to a small interval (0, λ*) and $p$ ≥ 2. We do not impose any symmetry hypothesis on the nonlinear potential. The constant-sign solutions are obtained by using variational techniques based on nonsmooth critical point theory (minimization argument, Mountain Pass theorem, and a Brezis-Nirenberg type result for C1-minimizers), while the nodal solution is constructed by an upper-lower solutions argument combined with the Zorn lemma and a nonsmooth second deformation theorem.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d33803baf7f0cb1b47f215f13049c4d5e426ae5a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance (2014, background): “So, as in Filippakis, Kristaly & Papageorgiou [21] (proof of Proposition 3.”