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 R3 composed of two non linear stationary Schrödinger equations (NLSEs), that is -∈2Δu + V(x)u = hv(u, v), -∈2Δv + V(x)v = hu(u, v). Under certain hypotheses on the potential V and the non linearity h, we manage to prove that there exists a solution (u∈, v∈) that decays ...
Cortopassi T., Georgiev V.
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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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The Nehari manifold for the Schrödinger–Poisson systems with steep well potential
Complex Variables and Elliptic Equations, 2018In this paper, via variational methods, we consider the existence and concentration of positive solutions for a system of Schrodinger–Poisson equation involving concave–convex nonlinearities under ...
Zhiqing Han, Qing-Jun Lou
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The Nehari manifold for nonlocal elliptic operators involving concave–convex nonlinearities
Zeitschrift für angewandte Mathematik und Physik, 2014In this paper, we study the multiplicity of solutions to equations driven by a nonlocal integro-differential operator $${{\mathcal{L}}_K}$$ with homogeneous Dirichlet boundary conditions.
Shengbing Deng +2 more
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The Nehari Manifold and its Application to a Fractional Boundary Value Problem
Differential Equations and Dynamical Systems, 2013In this paper, we study the Nehari manifold and its application to the following fractional boundary value problem: $$\begin{aligned} {\left\{ \begin{array}{ll} - \frac{d}{d t} \Big (\frac{1}{2} {}_0D_t^{- \beta } (u^{\prime } (t)) + \frac{1}{2} {}_tD_T^{- \beta } (u^{\prime } (t)
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The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent
Applied Mathematics and Computation, 2012Abstract In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system ( E λ , μ ) involving critical exponents and sign-changing weight functions.
Ching-yu Chen, Tsung-fang Wu
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The Nehari manifold for a semilinear elliptic equation involving a sublinear term
Calculus of Variations and Partial Differential Equations, 2004The Nehari manifold for the equation $$ -\Delta u(x) = \lambda u(x) + b(x) \vert u(x)\vert^{\gamma - 2} u(x) $$ for $ x \in \Omega $ together with Dirichlet boundary ...
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Non-Nehari manifold method for periodic discrete superlinear Schrödinger equation
Acta Mathematica Sinica, English Series, 2016We consider the nonlinear difference equations of the form $$Lu = f\left( {n,u} \right),\;n \in Z,$$ where L is a Jacobi operator given by (Lu)(n) = a(n)u(n+1)+a(n−1)u(n−1)+b(n)u(n) for n ∈ Z, {a(n)} and {b(n)} are real valued N-periodic sequences, and f(n, t) is superlinear on t. Inspired by previous work of Pankov [Discrete Contin. Dyn. Syst.,
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Nehari manifold and fractional Dirichlet boundary value problem
Analysis and Mathematical Physics, 2022J. Vanterler da C. Sousa +2 more
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