EXISTENCE OF A POSITIVE SOLUTION FOR SUPERLINEAR LAPLACIAN EQUATION VIA MOUNTAIN PASS THEOREM

EXISTENCE OF A POSITIVE SOLUTION FOR SUPERLINEAR LAPLACIAN EQUATION VIA MOUNTAIN PASS THEOREM

A. Keyhanfar, S. H. Rasouli, G. A. Afrouzi

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Abstract

In this paper, we are going to show a nonlinear laplacian equation with the Dirichlet boundary value as follow has a positive solution: where,
u = div(ru) is the laplacian operator, is a bounded domain in R3 with smooth boundary @ . At rst, we show the equation has a nontrivial solution. next, using strong maximal principle, Cerami condition and a variation of the mountain pass theorem help us to prove critical point of functional I is a positive solution.

Keywords

Laplacian equation; Postive solution; Cerami condition; Mountain pass the- orem.