In this article we consider the infinite semipositone problem in , a smooth bounded domain in , and u=0 on , where and , . Using stability analysis we prove the existence of a connected branch of maximal solutions emanating from infinity. Under certain additional hypothesis on the extremal solution at we prove a version of Crandall-Rabinowitz bifurcation theorem which provides a multiplicity result for .
Submitted May 3, 2018. Published November 1, 2018.
Math Subject Classifications: 35J25, 35J61, 35J75.
Key Words: Semipositone problems; topological methods; bifurcation theory.
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| Rajendran Dhanya |
School of Mathematics and Computer Science
Indian Institute of Technology
Goa 403401, India
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