Multiplicity of Positive Solutions for an Obstacle Problem in ℝ

  • Claudianor O. Alves
  • Francisco Julio S. A. Corrêa
Chapter
First Online:
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 85)

Abstract

In this paper we establish the existence of two positive solutions for the obstacle problem \( \int_\mathbb{R}[u^{\prime}(v-u)^{\prime}+(1+\lambda V(x))u(v-u)] \geq \int_\mathbb{R} f(u)(v-u),\forall v \ \in \; \mathbb{K} \) where f is a continuous function verifying some technical conditions and \( \mathbb{K} \) is the convex set given by \( \mathbb{K} = {v \in H^{1}(\mathbb{R});v \geq \varphi}, \) with \( {\varphi \in H^{1}(\mathbb{R})}, \) having nontrivial positive part with compact support in \( \mathbb{R} \)

Keywords

Obstacle problem variational methods positive solutions. 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Claudianor O. Alves
    • 1
  • Francisco Julio S. A. Corrêa
    • 1
  1. 1.Centro de Ciências e Tecnologia Unidade Acadêmica de Matemática e EstatísticaUniversidade Federal de Campina GrandeCampina GrandeBrazil

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