Abstract
We consider the elliptic problem in , , where is a smooth unbounded domain in , and . We use the shape of domain to prove that the above elliptic problem has a ground-state solution if the coefficient satisfies as and for some suitable constants , and . Furthermore, we prove that the above elliptic problem has multiple positive solutions if the coefficient also satisfies the above conditions, and , where is the best Sobolev constant of subcritical operator in and .
Citation
Tsung-Fang Wu. "Existence and Multiplicity of Positive Solutions for Dirichlet Problems in Unbounded Domains." Abstr. Appl. Anal. 2007 1 - 25, 2007. https://doi.org/10.1155/2007/18187
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