On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Advanced Nonlinear Studies - Tập 14 Số 3 - Trang 565-591 - 2014
Nikolaos S. Papageorgiou1, Patrick Winkert2
1Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
2Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

Tóm tắt

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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Thông tin xuất bản

Advanced Nonlinear Studies

Tập 14 Số 3

565-591

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