Electron. J. Diff. Equ., Vol. 2016 (2016), No. 229, pp. 1-9.

Existence of solutions for elliptic nonlinear problems on the unit ball of $\mathbb{R}^3$

Khadijah Sharaf

We consider an elliptic PDE with critical nonlinearity involving the Laplacian operator with zero Dirichlet boundary condition on the unit ball of $\mathbb{R}^3$. We assume some perturbation conditions and obtain what seems to be the first existence result for this problem.

Submitted March 8, 2016. Published August 23, 2016.
Math Subject Classifications: 35J65.
Key Words: Critical Sobolev exponent; critical points at infinity; variational method.

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Khadijah Sharaf
Department of mathematics
King Abdulaziz University, P.O. 80230
Jeddah, Kingdom of Saudi Arabia
email: kh_sharaf@yahoo.com

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