EXISTENCE RESULTS FOR A QUASILINEAR BOUNDARY VALUE PROBLEM INVESTIGATED VIA DEGREE THEORY

Authors

  • G.A. Afrouzi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
  • A. Hadjian Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
  • S. Shakeri Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
  • M. Mirzapour Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

In this article we prove the existence of at least one weak solution for the quasilinear problem
$$\left\{\begin{array}{ll} -\Delta_p u(x)=\lambda|u(x)|^{p-2}u(x)+h(x,u(x)) & \textrm{ in } \Omega,\\
u=0 & \textrm{ on } \partial \Omega \end{array}\right.$$
where $\Delta_p u:=\textrm{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian operator, $p>1$, $\Omega\subset \mathbb{R}^N$ is a non-empty bounded domain with Lipschitz boundary $(\Omega\in C^{0,1})$, $\lambda$ is a positive parameter and $h:\Omega\times \mathbb{R}\rightarrow \mathbb{R}$ is a bounded Carath\'{e}odory function. The approach is fully based on the degree theory.

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Published

2012-03-31

How to Cite

Afrouzi, G., Hadjian, A., Shakeri, S., & Mirzapour, M. (2012). EXISTENCE RESULTS FOR A QUASILINEAR BOUNDARY VALUE PROBLEM INVESTIGATED VIA DEGREE THEORY. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 3(1), 25-32. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/92

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Section

Research Article