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On the existence of positive entire solutions of nonlinear elliptic equations. (English) Zbl 0997.35019
Summary: Via non-smooth critical point theory, the author proves existence of entire positive solutions for a class of nonlinear elliptic problems \[ -\text{div}(\nabla_\xi{\mathcal L}(x,u,\nabla u))+D_s{\mathcal L}(x,u,\nabla u)+b(x)|u|^{p-2}u=g(x,u)\text{ in }\mathbb{R}^n, \] behaving asymptotically-like the \(p\)-Laplacian problem \[ -\text{div}(|\nabla u|^{p-2}\nabla u)+\lambda|u|^{p-2}u=u^{q-1}\text{ in }\mathbb{R}^n, \] for some suitable \(\lambda>0\) and \(q>p\), subjected to natural growth conditions.

35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
35J70 Degenerate elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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