Sublinear singular elliptic problems with two parameters

By Marius Ghergu, Vicentiu D. Rădulescu. 2003

106 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/58f4f2cdd27cd3dc03f75adbcb69153475370644

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

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].”
Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term (2005, background): “The asymptotic behaviour of the solution around the bifurcation point is also established, provided g(u) behaves like u−α around the origin, for some 0 α 1.”
Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type (2005, methodology): “The assumption ( g2) has been used in [14] and it implies the following Kelle Osserman-type growth condition around the origin:”
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.”
Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term (2006, background): “It is worth pointing out here that we do not assume any blow-up rate of decay on g around the origin (as in Ghergu and Rădulescu [12]) that may imply the property of compact support of Bénilan, Brezis and Crandall (see [4]).”
The asymptotic behaviour of the unique solution for the singular Lane–Emden–Fowler equation (2005, background): “The problem was discussed and extended to the more general problems in number of works; see, for instance, [2,9–17,19–21,23,28–33].”
Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient (2019, background): “For instance, Ghergu and Rădulescu [21] established several existence and nonexistence results for boundary value problems with singular term and parameters; Gasínski and Papageorgiou [20] studied a nonlinear Dirichlet problem with a singular term, a (p − 1)-sublinear term, and a Carathéodory pertur”
Lane-Emden-Fowler equations with convection and singular potential (2007, background): “Many papers have been devoted to the case p ≡ 1 and μ = 0 (see [10,12,15,28] and the references therein).”
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.”
Nonlinear nonhomogeneous singular problems (2019, result): “Previously, such bifurcation type results have been proved by Sun, Wu & Long [41], Haitao [18], Ghergu & Rădulescu [14, 15, 16] (semilinear problems driven by the Laplacian), and by Giacomoni, Schindler & Takač [17], Papageorgiou, Rădulescu & Repovš [35], Papageorgiou & Smyrlis [36], Papageorgiou, V”