This article is cited in 9 papers

Research Papers

Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer

S. B. Kolonitskiĭ

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

Abstract: The equation $-\Delta_pu=u^{q-1}$ with zero Dirichlet condition on the boundary is considered in a three-dimensional spherical layer. The existence of arbitrarily many distinct positive solutions in a sufficiently thin layer is proved.

Keywords: $p$-Laplacian, existence of many solutions.

Received: 22.09.2009

 English version: St. Petersburg Mathematical Journal, 2011, 22:3, 485–495

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