Nonlinear $p$-Laplacian problems on unbounded domains
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- by Lao Sen Yu PDF
- Proc. Amer. Math. Soc. 115 (1992), 1037-1045 Request permission
Abstract:
We consider the $p$-Laplacian problem \[ - div(a(x)|\nabla u{|^{p - 2}}\nabla u) + b(x)|u{|^{p - 2}}u = f(x,u),\quad x \in \Omega ,\quad u{|_{\partial \Omega }} = 0,\quad \lim \limits _{|x| \to \infty } u = 0,\] 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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 1037-1045
- MSC: Primary 35J40; Secondary 35B45, 35J65, 58E05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1162957-9
- MathSciNet review: 1162957