Sign-Changing and Extremal Constant-Sign Solutions of Nonlinear Elliptic Neumann Boundary Value Problems. (6th July 2010)

• Record Type: Journal Article
• Authors: Winkert, Patrick
• Other Names: Drábek Pavel Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-07-06
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/139126
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : Our aim is the study of a class of nonlinear elliptic problems under Neumann conditions involving thep -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 Fuc ̆ ik spectrum of thep -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.