Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615672 | Journal of Mathematical Analysis and Applications | 2015 | 13 Pages |
Abstract
Consider the following semilinear elliptic problem on B={x∈R2:|x|<1}B={x∈R2:|x|<1}{−Δu=λ1u+eu+f,in Bu=0on ∂B with f satisfying the following condition: f is smooth integrable radial and satisfies0<−∫Bfϕ1<8π, where ϕ1ϕ1 is the eigenfunction of (−Δ)(−Δ) corresponding to the first eigenvalue λ1λ1 in H01(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 equation with known solution with its degree. Connecting those two PDEs by homotopy and getting the uniform estimate for the connecting PDEs we shall achieve our result.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
B.B. Manna, P.N. Srikanth,