Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

By Marius Ghergu, Vicentiu D. Rădulescu. 2006

54 citations recorded by the source corpus.

Abstract We are concerned with singular elliptic equations of the form − Δ u = p ( x ) ( g ( u ) + f ( u ) + | ∇ u | a ) in R N ( N ⩾ 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6bfbfa265475953ec08c2a3f724866a96c5ba993

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations (2011, unknown): “In [15,16], Ghergu and Rădulescu studied the existence or the nonexistence of solutions for the following two elliptic problems with parameters ⎧⎨ ⎩ − u + K (x)g(u) = λ f (x, u) + μg(x, u), x ∈ Ω, u(x) > 0, x ∈ Ω, u(x) = 0, x ∈ ∂Ω, (4.”
Lane-Emden-Fowler equations with convection and singular potential (2007, result): “The results in this paper complete the study developed in [17,16,18] since here we deal with singular weights.”