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Existence and multiplicity of solutions for $p(x)$-Laplacian equations in $\Bbb R^N$. (English) Zbl 1134.35333
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.

35J60Nonlinear elliptic equations
35D05Existence of generalized solutions of PDE (MSC2000)
47J30Variational methods (nonlinear operator equations)
58E05Abstract critical point theory
Full Text: DOI
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