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The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms
Nonlinear Analysis, 2019Abstract In the present paper, we study the following singular Kirchhoff problem M ∬ R 2 N | u ( x ) − u ( y ) | 2 | x − y | N + 2 s d x d y ( − Δ ) s u = λ f ( x ) u − γ + g ( x ) u 2 s ∗ − 1 in Ω ,
Fiscella A, Mishra P
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Nehari manifold and fractional Dirichlet boundary value problem
Analysis and Mathematical Physics, 2022 J. Vanterler da C. Sousa +2 more
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Applicable Analysis, 2023
We consider the following class of elliptic problems \[ - \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\quad x\in {\mathbb{R}}^N, \] −ΔAu+u=aλ(x)|u|q−2u+bμ(x)|u|p−2u,x∈RN, where ...
Francisco Odair de Paiva +2 more
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We consider the following class of elliptic problems \[ - \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\quad x\in {\mathbb{R}}^N, \] −ΔAu+u=aλ(x)|u|q−2u+bμ(x)|u|p−2u,x∈RN, where ...
Francisco Odair de Paiva +2 more
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Transversality of stable and Nehari manifolds for a semilinear heat equation [PDF]
Calculus of Variations and Partial Differential Equations, 2011 It is well known that for the subcritical semilinear heat equation, negative initial energy is a sufficient condition for finite time blowup of the solution. We show that this is no longer true when the energy functional is replaced with the Nehari functional, thus answering negatively a question left open by Gazzola and Weth (2005). Our proof proceeds
Flávio Dickstein +3 more
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Nehari manifold for singular fractional p(x,.)-Laplacian problem
Complex Variables and Elliptic Equations, 2022In this paper, we consider a class of fractional Laplacian problems of the form: where is a bounded domain and is the fractional -Laplacian operator. We assume that λ and μ are positive parameters and is a continuous function.
R. Chammem, A. Ghanmi, A. Sahbani
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The Nehari manifold for double‐phase problems with convex and concave nonlinearities
Mathematische Nachrichten, 2023The aim of this paper is to establish the multiplicity of solutions for double‐phase problem. Employing the Nehari manifold approach, we show that the problem has at least two nontrivial solutions.
Qinghai Cao, B. Ge, Yu‐Ting Zhang
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Nehari manifold and existence of positive solutions to a class of quasilinear problems
Nonlinear Analysis: Theory, Methods & Applications, 2005Abstract In this paper, existence and multiplicity results to the following nonlinear elliptic equation: - Δ p u = λ | u | q - 2 u + | u | p * - 2 u , u > 0 in Ω ⊂ R N , together with mixed Dirichlet–Neumann or Neumann boundary conditions, are established. Here, Δ p
Alves, C.O., El Hamidi, Abdallah
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Infinite Sharp Conditions by Nehari Manifolds for Nonlinear Schrödinger Equations
The Journal of Geometric Analysis, 2019We study the Cauchy problem of nonlinear Schrodinger equation $$i\varphi _t+\Delta \varphi +|\varphi |^{p-1}\varphi =0$$. By constructing infinite Nehari manifolds with geometric features, we not only obtain infinite invariant sets of solutions, but also give infinite sharp conditions for global existence and finite time blow up of solutions.
Wei Lian +3 more
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A minimization problem with variable growth on Nehari manifold
Monatshefte für Mathematik, 2016In this paper, based on the theory of variable exponent space, we study a class of minimizing problem on Nehari manifold via concentration compactness principle. Under suitable assumptions, by showing a relative compactness of minimizing sequences, we prove the existence of minimizers.
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The Nehari manifold and application to a semilinear elliptic system
Nonlinear Analysis: Theory, Methods & Applications, 2009Abstract In this paper, we study the Nehari manifold and its application to the following semilinear elliptic system: { − Δ u + u = λ f ( x ) | u | q − 2 u , x ∈ Ω , − Δ v + v = μ g ( x ) | v | q − 2 v , x ∈ Ω , ∂ u ∂ n = α α + β h ( x )
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