EXISTENCE OF A POSITIVE SOLUTION FOR SUPERLINEAR LAPLACIAN EQUATION VIA MOUNTAIN PASS THEOREM - Keyhanfar, A; Rasouli, S.H; Afrouzi, G.A (TWMS journal of applied and engineering mathematics, 2020)
In this paper, we are going to show a nonlinear laplacian equation with the Dirichlet boundary value as follow has a positive solution: [mathematical expression not reproducible] where, [DELTA]u = div([nabla]u) is the laplacian operator, [OMEGA] is a bounded domain in [R.sup.3] with smooth boundary [partial derivative][OMEGA]. At first, 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 theorem. AMS Subject Classification: 83-02, 99A00