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Zbl 1134.35333
Fan, Xianling; Han, Xiaoyou
Existence and multiplicity of solutions for $p(x)$-Laplacian equations in $\Bbb R^N$.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 59, No. 1-2, A, 173-188 (2004). ISSN 0362-546X

Summary: This paper investigates the existence and multiplicity of solutions for $p(x)$-Laplacian equations $-\mathrm{div}(|\nabla u|^{p(x)-2}\nabla u) + |u|^{p(x)-2}u = f(x,u)$ in $\Bbb R^N$, $u\in W^{1,p(x)}(\Bbb R^N)$ in the cases corresponding to sublinear", superlinear" and concave-convex nonlinearity" if $p=2$. They apply critical point theory in certain Sobolev spaces fitted to the problem.
MSC 2000:
*35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE
47J30 Variational methods
58E05 Abstract critical point theory

Keywords: $p(x)$-Laplacian; Generalized Sobolev space; Critical point; Genus theory

Cited in: Zbl 1142.35018

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