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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter
Fractional Calculus and Applied Analysis, 2023 In this work we study the following nonlocal problem $$\begin{aligned} \left\{ \begin{aligned} M(\Vert u\Vert ^2_X)(-\varDelta )^s u&= \lambda {f(x)}|u|^{\gamma -2}u+{g(x)}|u|^{p-2}u{} & {} \text{ in }\ \ \varOmega , \\ u&=0{} & {} \text{ on }\ \ \mathbb
P. Mishra, V. M. Tripathi
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A generalised Nehari manifold method for a class of non-linear Schrödinger systems in ℝ3
AIP Conference Proceedings, 2022We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schr\"odinger equations (NLSEs), that is $-\epsilon^2 \Delta u + V(x) u= h_v(u,v), - \epsilon^2 \Delta v + V(x) v=
Tommaso Cortopassi, Vladimir Georgiev
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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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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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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 and bifurcation for a ψ‐Hilfer fractional p‐Laplacian
Mathematical methods in the applied sciences, 2021In this paper, we discuss the bifurcation from infinity for nonlinear problem with a fractional p‐Laplacian in ψ‐fractional space ℍpα,β;ψ , whose bifurcation is directly linked to the signal ∫0Tb(x)ϕ1q+1dx with 1
J. Sousa
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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, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. El Hamidi, Claudianor O. Alves
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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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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 ,
A. Fiscella, P. Mishra
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