Nonlinear Elliptic Equations with Neumann Boundary Conditions
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This chapter aims to present relevant knowledge regarding recent progress on nonlinear elliptic equations with Neumann boundary conditions. In fact, all the results presented here bring novelties with respect to the available literature. We emphasize the specific functional setting and techniques involved in handling the Neumann problems, which are distinct in comparison with those for the Dirichlet problems. The first section of the chapter discusses the multiple solutions that arise at near resonance, from the left and from the right, in the Neumann problems depending on parameters. The second section focuses on nonlinear Neumann problems whose differential part is described by a general nonhomogeneous operator. The third section builds a common approach for both sublinear and superlinear cases of semilinear Neumann problems. Related comments and references are given in a remarks section.
KeywordsNeumann Problem Morse Theory Critical Point Theory Multiplicity Result Hemivariational Inequality
- 304.Motreanu, D., Motreanu, V.V., Papageorgiou, N.S.: Existence and nonexistence of positive solutions for parametric Neumann problems with p-Laplacian. Tohoku Math. J. (to appear)Google Scholar