Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774168 | Journal of Differential Equations | 2017 | 28 Pages |
Abstract
We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem{Îu+(a+(|x|)âμaâ(|x|))g(u)=0,|x|<1,u(x)ââ,|x|â1, where g is a function superlinear at zero and at infinity, a+ and aâ are the positive/negative part, respectively, of a sign-changing function a and μ>0 is a large parameter. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function a. The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions toÎu+(a+(|x|)âμaâ(|x|))g(u)=0,xâRN, is also considered.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alberto Boscaggin, Walter Dambrosio, Duccio Papini,