Existence of a positive solution for superlinear Laplacian equation via mountain pass theorem
Künye
Keyhanfar, A., Rasouli, S. H. & Afrouzi, G. A. (2020). Existence of a positive solution for superlinear Laplacian equation via mountain pass theorem. TWMS Journal Of Applied And Engineering Mathematics, 10(3), 799-805Özet
In this paper, we are going to show a nonlinear laplacian equation with the Dirichlet boundary value as follow has a positive solution: ( −∆u + V (x)u = g(x, u) x ∈ Ω u = 0 x ∈ ∂Ω where, ∆u = div(∇u) is the laplacian operator, Ω is a bounded domain in R³ with smooth boundary ∂Ω. 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.
Kaynak
TWMS Journal Of Applied And Engineering MathematicsCilt
10Sayı
3Bağlantı
http://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/2867http://jaem.isikun.edu.tr/web/index.php/archive/106-vol10no3/574
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