The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent
Applied Mathematics and Computation, 2012The authors study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system of the type \[ \begin{cases} -\Delta u=f_\lambda(x)|u|^{q-2}u+{\alpha\over{\alpha+\beta}}h(x)|u|^{\alpha-2}u|v|^\beta &\text{in}\;\Omega,\\ -\Delta v=g_\mu(x)|v|^{q-2}v+{\beta\over{\alpha+\beta}}h(x)|u ...
Tsung-Fang Wu
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Transversality of stable and Nehari manifolds for a semilinear heat equation
Calculus of Variations and Partial Differential Equations, 2011Let \(\Omega\) be a smooth bounded domain in \({\mathbb R}^n\) and \(p>1\); \(p2\). Consider the semilinear heat equation \(u_t-\Delta u=|u|^{p-1}u\) for \(x\in\Omega\), \(t>0\), complemented by the boundary conditions \(u=0\) for \(x\in\partial\Omega\), \(t>0\), and the initial condition \(u(x,0)=u_0(x)\) for \(x\in\Omega\), where \(u_0\in H^1_0 ...
Dickstein, Flavio +3 more
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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 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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On a minimization problem involving fractional Sobolev spaces on Nehari manifold
Afrika Matematika, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Nehari Manifold and its Application to a Fractional Boundary Value Problem
Differential Equations and Dynamical Systems, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ground state and multiple solutions via generalized Nehari manifold
Nonlinear Analysis: Theory, Methods & Applications, 2014In this paper, the authors study a class of superlinear elliptic equations \[ -\Delta u+V(x)u=f(x,u),\;u\in H^{1}_{0}(\Omega) \] where \(\Omega\subset\mathbb R^{N}\) is a periodic domain, i.e. there exist a partition \((Q_{m})_{m\geq 1}\) of \(\Omega\) and a sequence of points \((y_{m})_{m\geq 1}\subset\mathbb R^{N}\) such that (i) \((y_{m})_{m\geq 1}\)
Zhong, Xuexiu, Zou, W.
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NON-NEHARI-MANIFOLD METHOD FOR ASYMPTOTICALLY LINEAR SCHRÖDINGER EQUATION
Journal of the Australian Mathematical Society, 2014AbstractWe 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}(-\
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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.
Alves, C. O., El Hamidi, A.
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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 ...
Qing-Jun Lou, Zhi-Qing Han
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The Nehari manifold for a fractional p-Laplacian system involving concave–convex nonlinearities
Nonlinear Analysis: Real World Applications, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Wenjing, Deng, Shengbing
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