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

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...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 10; no. 3; p. 799
Main Authors Keyhanfar, A, Rasouli, S.H, Afrouzi, G.A
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2020
Elman Hasanoglu
Subjects
Boundary value problems
Critical point
Dirichlet problem
Existence theorems
Laplace equation
Laplacian operator
Mathematical research
Mountains
Smooth boundaries
Theorems
Iran
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Summary: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
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:2146-1147
2146-1147