On a class of sublinear singular elliptic problems with convection term

By Marius Ghergu, Vicentiu D. Rădulescu. 2005

61 citations recorded by the source corpus.

Abstract We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem − Δ u + K ( x ) g ( u ) + | ∇ u | a = λ f ( x , u ) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N ( N ⩾ 2 ) is a smooth bounded domain, 0 a ⩽ 2 , λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term | ∇ u | a . Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/16ef89eb42ff8e1b7c46467d34bf2fb0c3dfa87e

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

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.”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “multiplicity results for the Laplacian and the p-Laplacian with singular non-linearity, see [1, 11, 14, 18, 20, 23, 24].”
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases (2011, background): “Problems of this kind are discussed in many papers; see, for instance, [5, 6, 8, 9, 11, 12] and references therein.”
Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term (2006, background): “, Ghergu and Rădulescu [14,15]), due to the lack of an adequate comparison principle.”
Positive solutions of the p-Laplace equation with singular nonlinearity (2009, methodology): “We refer the reader to the papers [6,7,9,10,13,17,20,22,30–32,34] for work related to singular boundary value problems when p = 2.”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, result): “Our main results (see Ghergu and Rădulescu [47]) are the following.”