Abstract
We study the existence of a weak solution for a semilinear elliptic Dirichlet boundary-value problem \begin{align*} Lu(x)-\mu u g_1(x)+h(u)g_2(x)&=f(x)\quad \mbox{in }\Omega,\\ u(x)&=0\qquad \mbox{ on }\partial\Omega, \end{align*} in a suitable weighted Sobolev space, where $\Omega=\mathbb{R} ^n\backslash K,n\geq3$ is an unbounded domain, and where $K$ is a closure of some bounded domain in $\mathbb{R}^n,n\geq3$.
Citation
Rasmita Kar. "Applications of monotone operators to a class of semilinear elliptic BVPs in unbounded domain." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 291 - 301, may 2014. https://doi.org/10.36045/bbms/1400592626
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