The Nehari manifold for fractional systems involving critical nonlinearities
Communications on Pure and Applied Analysis, 2015 To appear in Commun.
Xiaoming He +2 more
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Nehari manifold and fractional Dirichlet boundary value problem
Analysis and Mathematical Physics, 2022 J. Sousa, N. Nyamoradi, M. Lamine
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The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition
Nonlinear Analysis: Modelling and Control, 2007 The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)|p−2 + b(x)|u(x)|γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form of t → J(tu) where J is the Euler functional associated with the ...
G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh
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Nehari manifold method for singular double phase problem with optimal control on parameter [PDF]
Journal of Mathematics and Physics, 2023 In this paper, we consider the following singular double phase problem −div(|∇u|p−2∇u + a(x)|∇u|q−2∇u) = λf(x)u−γ + g(x)ur−1, u > 0 in Ω and u = 0 on ∂Ω, where Ω⊂RN is an open bounded domain with smooth boundary, dimension N ≥ 2, exponents p < q < r < p*
Alessio Fiscella +2 more
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Existence of Solutions for a Singular Double Phase Problem Involving a $$\psi $$ ψ -Hilfer Fractional Operator Via Nehari Manifold [PDF]
Qualitative Theory of Dynamical Systems, 2023 In this present paper, we investigate a new class of singular double phase p -Laplacian equation problems with a $$\psi $$ ψ -Hilfer fractional operator combined from a parametric term.
J. Vanterler +3 more
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The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative [PDF]
Advances in Differential Equations, 2018 We aim to investigate the following nonlinear boundary value problems of fractional differential equations: (Pλ){−tD1α(|0Dtα(u(t))|p−20Dtαu(t))=f(t,u(t))+λg(t)|u(t)|q−2u(t)(t∈(0,1)),u(0)=u(1)=0, $$\begin{aligned} (\mathrm{P}_{\lambda}) \left ...
Kamel Saoudi +4 more
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NON-NEHARI-MANIFOLD METHOD FOR ASYMPTOTICALLY LINEAR SCHRÖDINGER EQUATION [PDF]
Journal of the Australian Mathematical Society, 2014 AbstractWe consider the semilinear Schrödinger equation$$\begin{eqnarray}\left\{\begin{array}{@{}l@{}}-\triangle u+V(x)u=f(x,u),\quad x\in \mathbb{R}^{N},\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{eqnarray}$$where$f(x,u)$is asymptotically linear with respect to$u$,$V(x)$is 1-periodic in each of$x_{1},x_{2},\dots ,x_{N}$and$\sup [{\it\sigma}(-\
Xianhua Tang
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Second-order derivative of domain-dependent functionals along Nehari manifold trajectories [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2019 Assume that a family of domain-dependent functionals EΩt possesses a corresponding family of least energy critical points ut which can be found as (possibly nonunique) minimizers of EΩt over the associated Nehari manifold N(Ωt). We obtain a formula for the second-order derivative of EΩt with respect to t along Nehari manifold trajectories of the form ...
Vladimir Bobkov, Sergey Kolonitskii
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The Nehari manifold for a degenerate logistic parabolic equation
, 2023 The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison principle in order to study the evolutionary dynamics.
Juliana Dumêt Fernandes +1 more
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Non-Nehari manifold method for asymptotically periodic Schrödinger equations [PDF]
Science China Mathematics, 2014 We consider the semilinear Schr dinger equation $$ \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\R}^{N}, u\in H^{1}({\R}^{N}), \end{array} \right. $$ where $f$ is a superlinear, subcritical nonlinearity. We mainly study the case where $V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbb{R}^N)$, $V_0(x)$ is 1-periodic in each of $x_1, x_2 ...
Xianhua Tang
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