Lane-Emden-Fowler equations with convection and singular potential

By Louis Dupaigne, Marius Ghergu, Vicentiu D. Rădulescu. 2007

92 citations recorded by the source corpus.

Abstract We are concerned with singular elliptic problems of the form − Δ u ± p ( d ( x ) ) g ( u ) = λ f ( x , u ) + μ | ∇ u | a in Ω, where Ω is a smooth bounded domain in R N , d ( x ) = dist ( x , ∂ Ω ) , λ > 0 , μ ∈ R , 0 a ⩽ 2 , and f is a nondecreasing function. We assume that p ( d ( x ) ) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p ( d ( x ) ) , the convection term | ∇ u | a , and the singular nonlinearity g, we establish various existence and nonexistence results.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d5d9752f5dde2b4ff4cc0d204287d77f3c62790

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Citations in the corpus

On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “Several authors considered problems of Lane–Emden–Fowler type with singular non-linearity, see [10, 15, 19].”
A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations (2011, unknown): “The theory of singular elliptic boundary value problems for partial differential equations has become an important area of investigation in the past three decades, see [10,11,13–17,20,24,26,32,33,41] and references therein.”
Existence and uniqueness results for double phase problems with convection term (2019, methodology): “For other existence results on quasilinear equations with convection term and the p-Laplace or the (p, q)-Laplace differential operator we refer to the papers of Bai-Gasiński-Papageorgiou [6], De Figueiredo-Girardi-Matzeu [12], Dupaigne-Ghergu-Rădulescu [13], Faraci-MotreanuPuglisi [14], Faria-Miyag”
Lane–Emden systems with negative exponents (2010, unknown): “5 in [4] (see also [12, Section 9]).”
Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient (2019, background): “[12], Kaufmann and Medri [25], D’Ambrosio and Mitidieri [9], Carl et al.”