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Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term. (English) Zbl 1211.35128

Summary: We are concerned with singular elliptic equations of the form \(-\Delta u=p(x)(g(u)+f(u)+|\nabla u|^a)\) in \(\mathbb R^N\) \((N\geq 3)\), where \(p\) is a positive weight and \(0<a<1\). Under the hypothesis that \(f\) is a nondecreasing function with sublinear growth and \(g\) is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.

MSC:

35J75 Singular elliptic equations
35B50 Maximum principles in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B40 Asymptotic behavior of solutions to PDEs
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