Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type

By Florica Şt. Cîrstea, Marius Ghergu, Vicentiu D. Rădulescu. 2005

92 citations recorded by the source corpus.

We are concerned with the generalized Lane–Emden–Fowler equation −�u = λf (u) + a(x)g(u) in Ω, subject to the Dirichlet boundary condition u|∂Ω = 0, where Ω is a smooth bounded domain in R N , λ ∈ R, a is a nonnegative Holder function, and f is positive and nondecreasing such that the mapping f( s)/sis nonincreasing in (0, ∞). Here, the singular character of the problem is given by the nonlinearity g which is assumed to be unbounded around the origin. We distinguish two different cases which are related to the sublinear (respectively linear) growth of f at infinity.  2004 Elsevier SAS. All rights reserved.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/960dd916425922e5739f9c284a5d4a4c86cd7d60

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term (2006, methodology): “In this sense, we refer the reader to Callegari and Nachman [5], Cîrstea, Ghergu and Rădulescu [6], Coclite and Palmieri [8], Crandall, Rabinowitz and Tartar [9], Díaz, Morel, and Oswald [10], Ghergu and Rădulescu [13], Shi and Yao [21].”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, methodology): “Our main results (see Ghergu and Rădulescu [47]) are the following.”
Combined effects in nonlinear problems arising in the study of anisotropic continuous media (2016, background): “The framework discussed in [15] includes the case f(t) = tp and g(t) = t−γ , where 0 < p ≤ 1 and 0 < γ < 1.”
Lane-Emden-Fowler equations with convection and singular potential (2007, background): “Such singular boundary value problems arise in the context of chemical heterogeneous catalysts and chemical catalyst kinetics, in the theory of heat conduction in electrically conducting materials, singular minimal surfaces, as well as in the study of non-Newtonian fluids or boundary layer phenomena”
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].”
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].”