Existence Solution For Class Of P-laplacian Equations

Volume 4, Issue 1, pp 53 - 59

Publication Date: 2012-01-18

Authors

Malihe Bagheri - Department of mathematic, Golestan Institute of Higher Education,Golestan Province,Iran.
Mahnaz Bagheri - Department of mathematice, Islamic Azad University, behshar Branch, Iran.

Abstract

We study existence of positive solution of the equation \[-\Delta_pu=\lambda|u|^{p-2}u+f(x,u)\] with zero Dirichlet boundary conditions in bounded domain \(\Omega\in \mathbb{R}^n\) where \(\Delta_p\) denotes the p-laplacian operator defined by \(-\Delta_pz=div(|\nabla z|^{p-2}\nabla z); p,\lambda\in \mathbb{R}\) and \(p>1\).Our main result establishes the existence of weak solution.

Keywords

p-laplacian, weak solution, homogenous.

References

1. P.Drabek and y. Hung Bifurcation problems for the p-Laplacian in \(\mathbb{R}^n\). Trans. Amer.Math .Soe.
2. p.Drabek and Y. Hung. Multiple positive solutions of quasilinear elliptic equations in \(\mathbb{R}^n\).Nonlinear.Anal.Theory,Meth.and Appl.
3. S.I.Pohozaev. On one approach to nonlinear equations .Dokl.Akad.Nauk 247 (1979), 1327 31.
4. S.I.Pohozaev. On fibering method for the solution of nonlinear boundary value problems.Trudy Mat.Inst.Steklov.192 (1990), 140-63.
5. A.Anane simplicite et isolation de la premiere valeure proper du p-Laplacian avec poids.C.R.Acad.Sci.Paris Ser.I 305(1987), 725-8.
6. G.Barles. Remarks on uniqueness results of the first eigenvalue of the p-Laplacian. Ann.Fac.Sci.Toulouse9 (1988), 76-75.

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