# On a problem of resonance with exponential non linearity

- Authors
- Type
- Preprint
- Publication Date
- Submission Date
- Identifiers
- arXiv ID: 1405.0862
- Source
- arXiv
- License
- Yellow
- External links

## Abstract

We have considered the following semi linear elliptic problem on the unit disk $B$ $-\Delta u = \lambda_1 u+e^u+f $ in $B$ with the Dirichlet boundary condition and $f$ satisfying the following condition : $f\in L^r(B)$, for some $r>2$ and $-\int_B f\phi_1<4\pi$. Where $\phi_1$ is the eigen function of $(-\Delta)$ corresponding to the first eigenvalue $\lambda_1$ in $H_0^1(B)$. We shall find the existence of a radial solution of this PDE. We shall use degree theory to get the existence starting from a suitable with known solution with its degree. Connecting those two PDE's by homotopy and getting the uniform estimate for the connecting PDE's we shall achieve our result.