Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nonlinear $ p$-Laplacian problems on unbounded domains


Author: Lao Sen Yu
Journal: Proc. Amer. Math. Soc. 115 (1992), 1037-1045
MSC: Primary 35J40; Secondary 35B45, 35J65, 58E05
MathSciNet review: 1162957
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Abstract: We consider the $ p$-Laplacian problem

$\displaystyle - div(a(x)\vert\nabla u{\vert^{p - 2}}\nabla u) + b(x)\vert u{\ve... ...al \Omega }} = 0,\quad \mathop {\lim }\limits_{\vert x\vert \to \infty } u = 0,$

where $ 1 < p < n,\Omega ( \subset {R^n})$ is an exterior domain. Under certain conditions, we show the existence of solutions for this problem via critical point theory.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1162957-9
Keywords: $ p$-Laplacian problems, decaying solutions
Article copyright: © Copyright 1992 American Mathematical Society