On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Nikolaos S. Papageorgiou 1  and Patrick Winkert 2
  • 1 Department of Mathematics National Technical University, Zografou Campus, Athens 15780, Greece
  • 2 Institut für Mathematik Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

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.

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Advanced Nonlinear Studies (ANS)  is aimed at publishing scholarly articles on nonlinear problems, particularly those involving Differential and Integral  Equations, Dynamical Systems, Calculus of Variations, and related areas. It will also publish novel and interesting applications of these areas to problems in biology,  engineering,  materials sciences,  physics and other  sciences.

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