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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