Elliptic Problems with Non Lipschitz Nonlinearities: Some Recent Results and Open Questions

Authors

  • Giovanni Anello Author

Keywords:

Elliptic boundary value problem, nonnegative solution, positive solution, least en ergy solution, least energy nodal solution, variational methods, indefinite nonlinearities

Abstract

 Let p ∈]1,+∞[, let r,s ∈]0,p[, with r < s, and let λ ∈]0,+∞[. In this paper, we present some  recent existence and multiplicity results on the solutions of the Dirichlet problem for the elliptic equation −∆pu = (λ|u|s−2u−|u|r−2u)χ{u=0} in a bounded domain Ω ⊂ RN, with 0-boundary data. Some related open questions are also proposed.

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Published

2017-01-02

Issue

Vol. 2 No. 1 (2017): volume 2 issue 1 (2017)

Section

Articles

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How to Cite

Elliptic Problems with Non Lipschitz Nonlinearities: Some Recent Results and Open Questions. (2017). Minimax Theory and Its Applications, 2(1), 1-7. https://journalmta.com/index.php/jmta/article/view/5