EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Document Type : Regular Paper

Authors

Department of Mathematics, Faculty of Basic Sciences Mazandaran University, Babolsar, I. R. of Iran

Abstract

We consider the semilinear elliptic boundary value problem
  
= ∈∂Ω
− Δ = ∈Ω
u x x
u x f u x x
( ) 0;
( ) λ ( ( ));
where λ > 0 is a parameter, Ω is a bounded region in RN with a smooth boundary, and f is a
smooth function. We prove, under some additional conditions, the existence of a positive solution for λ
large. We prove that our solution u for λ large is such that = →∞
∈Ω
|| u ||: sup| u(x) |
x
as λ →∞.
Also, in the case of N = 1, we use a bifurcation theory to show that the solution is unstable.

Keywords

Iranian Journal of Science
Volume 29, Issue 2 - Serial Number 2
September and October 2005
Pages 296-304

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