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BY-NC-ND 4.0 license Open Access Published by De Gruyter March 10, 2016

On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Nikolaos S. Papageorgiou and Patrick Winkert

Abstract

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.

Published Online: 2016-03-10
Published in Print: 2014-08-01

© 2016 by Advanced Nonlinear Studies, Inc.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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