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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 14, Issue 3


On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Nikolaos S. Papageorgiou / Patrick Winkert
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2014-0303


We study a nonlinear parametric elliptic equation (nonlinear eigenvalue problem) driven by a nonhomogeneous differential operator. Our setting incorporates equations driven by the p-Laplacian, the (p, q)-Laplacian, and the generalized p-mean curvature differential operator. Applying variational methods we show that for λ > 0 (the parameter) sufficiently large the problem has at least three nontrivial smooth solutions whereby one is positive, one is negative and the last one has changing sign (nodal). In the particular case of (p, 2)-equations, using Morse theory, we produce another nodal solution for a total of four nontrivial smooth solutions.

Keywords: Constant sign and nodal solutions; nonlinear regularity; critical point of mountain pass type; extremal solutions; local minimizers; maximum principle

About the article

Published Online: 2016-03-10

Published in Print: 2014-08-01

Citation Information: Advanced Nonlinear Studies, Volume 14, Issue 3, Pages 565–591, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2014-0303.

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