Extremal, Nodal and Stable Solutions for Nonlinear Elliptic Equations-Reference-Cited by-同舟云学术

Extremal, Nodal and Stable Solutions for Nonlinear Elliptic Equations

Published:2015-08-01 Issue:3 Volume:15 Page:629-665
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Gasiński Leszek¹,Papageorgiou Nikolaos S.²

Affiliation:

1. Faculty of Mathematics and Computer Science Jagiellonian University ul. Lojasiewicza 6, 30348 Kraków, Poland

2. Department of Mathematics National Technical University, Zografou Campus Athens 15780, Greece

Abstract

Abstract We consider Dirichlet p-Laplacian equations which may be resonant with respect to the principal eigenvalue at ±∞. We show the existence of extremal nontrivial constant sign solutions and of nodal solutions. In the semilinear case (p = 2) we produce additional nodal solutions. We show that certain parametric equations (eigenvalue problems) studied in the past, are a special case of our multiplicity theorem. Finally, we establish the stability of the extremal solutions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-0306/pdf

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