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Nonlinear Elliptic Equations with Neumann Boundary Conditions

In: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author

Listed:
  • Dumitru Motreanu

    (University of Perpignan, Department of Mathematics)

  • Viorica Venera Motreanu

    (Ben-Gurion University of the Negev, Department of Mathematics)

  • Nikolaos Papageorgiou

    (National Technical University, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Dumitru Motreanu & Viorica Venera Motreanu & Nikolaos Papageorgiou, 2014. "Nonlinear Elliptic Equations with Neumann Boundary Conditions," Springer Books, in: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, edition 127, chapter 0, pages 387-436, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-9323-5_12
    DOI: 10.1007/978-1-4614-9323-5_12
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