Nonlinear Analysis - Theory and Methods

Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan

doi:10.1007/978-3-030-03430-6

Cited by 410 publications

(267 citation statements)

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“…In recent years, there has been a great deal of work done on problem (1.1), especially concerning the existence, multiplicity, uniqueness and regularity of solutions. Some important and interesting results can be found, for example, in [4,5,3,2,7,10,8,11,12,13,15,18,21,19,22,23,24,25,29,30,31,32,33,40] and references therein.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 95%

Existence and multiplicity results for a newp(x)-Kirchhoff problem

et al. 2020

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 95%

Existence and multiplicity results for a newp(x)-Kirchhoff problem

et al. 2020

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“…where W and g are continuous functions, have also attracted increasing attention to the existence of positive solutions, negative solutions, sign-changing solutions, multiple solutions, and ground states and semiclassical states via variational methods, see for example Bahrouni et [30][31][32][33][34][35][36][37] and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Least energy nodal solutions for Kirchhoff‐type Laplacian problems

Cheng

Chen

Zhang

2020

Math Methods in App Sciences

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In this paper, we are concerned with the existence of least energy nodal solutions for the following Kirchhoff‐type Laplacian problems: {left leftarray−M∫Ω|∇u|2dxΔu=g(u),arrayx∈Ω;arrayu=0,arrayx∈∂Ω, where normalΩ⊂double-struckRN is a bounded domain with a smooth boundary ∂normalΩ, N=1,2,3, Mfalse(tfalse)=a+btα,a,α>0,b≥0, and g∈scriptCfalse(double-struckR,double-struckRfalse). In the light of characteristics of the Kirchhoff‐type function M, we impose a weaker assumption on g instead of the usual Nehari type monotonicity condition and then prove the existence of one least energy nodal solution ub of Equation by applying constraint variational method, quantitative deformation lemma as well as one variant of Miranda theorem. Moreover, we show that the energy of nodal solution ub is strictly larger than twice of that of any ground state solutions of Nehari type to Equation and also study the convergence property of ub as the parameter b↘0. Our results improve and extend the known results of the usual case α=1 in the sense that a more wider rang of α is covered.

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“…We say that ϕ(·) satisfies the "C-condition", if the following property holds "Every sequence {u n } n 1 ⊆ X such that {ϕ(u n )} n 1 ⊆ R is bounded and (1 + ||u n || X )ϕ ′ (u n ) → 0 in X * as n → ∞, admits a strongly convergent subsequence". This is a compactness-type condition on the functional ϕ and it leads to the minimax theory of the critical values of ϕ (see, for example, Papageorgiou, Rȃdulescu & Repovš [12]).…”

Section: Preliminaries and Hypothesesmentioning

confidence: 99%

Positive solutions for a class of singular Dirichlet problems

Papageorgiou

Rădulescu

Repovš

2019

Journal of Differential Equations

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We consider a Dirichlet elliptic problem driven by the Laplacian with singular and superlinear nonlinearities. The singular term appears on the left-hand side while the superlinear perturbation is parametric with parameter λ > 0 and it need not satisfy the AR-condition. Having as our starting point the work of Diaz-Morel-Oswald (1987), we show that there is a critical parameter value λ * such that for all λ > λ * the problem has two positive solutions, while for λ < λ * there are no positive solutions. What happens in the critical case λ = λ * is an interesting open problem.

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Nonlinear Analysis - Theory and Methods

Cited by 410 publications

References 0 publications

Existence and multiplicity results for a newp(x)-Kirchhoff problem

Existence and multiplicity results for a newp(x)-Kirchhoff problem

Least energy nodal solutions for Kirchhoff‐type Laplacian problems

Positive solutions for a class of singular Dirichlet problems

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