Sign-Changing and Extremal Constant-Sign Solutions of Nonlinear Elliptic Neumann Boundary Value Problems
Our aim is the study of a class of nonlinear elliptic problems under Neumann conditions involving the p-Laplacian. We prove the existence of at least three nontrivial solutions, which means that we get two extremal constant-sign solutions and one sign-changing solution by using truncation techniques...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2010/139126 |
| Summary: | Our aim is the study of a class of nonlinear elliptic problems under Neumann conditions involving the p-Laplacian. We prove the existence of at least three nontrivial solutions, which means that we get two extremal constant-sign solutions and one sign-changing solution by using truncation techniques and comparison principles for nonlinear elliptic differential inequalities. We also apply the properties of the Fuc̆ik spectrum of the p-Laplacian and, in particular, we make use of variational and topological tools, for example, critical point theory, Mountain-Pass Theorem, and the Second Deformation Lemma. |
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| ISSN: | 1687-2762 1687-2770 |