Combined effects in nonlinear problems arising in the study of anisotropic continuous media

Repovš, Dušan; Rădulescu, Vicenţiu D.

doi:10.1016/j.na.2011.01.037

Cited by 96 publications

(54 citation statements)

References 30 publications

(27 reference statements)

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“…On the other hand, Radulescu and Repovs studied in [17] the competition between convex and concave nonlinearities by considering problem (1.2), with 1 < < 0 and p > 1. Such problems arise in the study of anisotropic continuous media.…”

Section: Introductionmentioning

confidence: 99%

Combined effects in nonlinear singular elliptic problems in a bounded domain

Chemmam

Mâagli

Masmoudi

et al. 2012

Advances in Nonlinear Analysis

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We establish an existence result of positive solutions to the following boundary value problem:where is a bounded C 1;1 -domain in R n ,˛1;˛2 < 1 and a 1 ; a 2 are nonnegative functions in C loc . /, 0 < < 1, satisfying some appropriate assumptions related to Karamata regular variation theory. We give estimates on such solutions where appear the combined effects of singular and sublinear terms in the nonlinearity.

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Section: Introductionmentioning

confidence: 99%

Combined effects in nonlinear singular elliptic problems in a bounded domain

Chemmam

Mâagli

Masmoudi

et al. 2012

Advances in Nonlinear Analysis

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“…p-Laplacian case. Extensions to equations involving more general reactions, were obtained by Gasinski and Papageorgiou [13], Hu and Papageorgiou [15] and Rȃdulescu and Repovš [22]. Other problems with competition phenomena, can be found in the works of Cîrstea, Ghergu and Rȃdulescu [4] (problems with singular terms) and of Kristaly and Moroşanu [16] (problems with oscillating reaction).…”

mentioning

confidence: 99%

Bifurcation of positive solutions for nonlinear nonhomogeneous Robin and Neumann problems with competing nonlinearities

Papageorgiou¹,

Rădulescu²

2015

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper we deal with Robin and Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing nonlinearities (concave-convex nonlinearities). For the Robin problem and without employing the Ambrosetti-Rabinowitz condition, we prove a bifurcation theorem for the positive solutions for small values of the parameter λ > 0. For the Neumann problem with a different geometry and using the Ambrosetti-Rabinowitz condition we prove bifurcation for large values of λ > 0.2010 Mathematics Subject Classification. 35J66, 35J70, 35J92.

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“…Such bifurcation type results, were proved by Brock et al [3], Filippakis et al [8], Gasinski and Papageorgiou [10], Rȃdulescu and Repovs [17], Takeuchi [19,20] (semilinear or nonlinear Dirichlet problems) and by Cardinali et al [4], Papageorgiou and Rȃdulescu [15] (for nonlinear Neumann problems). All the aforementioned results impose more restrictive conditions on the reaction f (z, ·).…”

Section: Introductionmentioning

confidence: 77%