On a problem of resonance with exponential non linearity

B. B. Manna; P. N. Srikanth

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arXiv · 1405.0862

On a problem of resonance with exponential non linearity

B. B. Manna·P. N. Srikanth

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Abstract

We have considered the following semi linear elliptic problem on the unit disk $B$ $-Δu = λ_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 $-\int_B fϕ_1<4π$. Where $ϕ_1$ is the eigen function of $(-Δ)$ corresponding to the first eigenvalue $λ_1$ 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.

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B. B. Manna, P. N. Srikanth. 2016-05-09. On a problem of resonance with exponential non linearity. https://arxiv.org/abs/1405.0862

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