Results 151 to 160 of about 262,340 (175)

Ground state and multiple solutions via generalized Nehari manifold

Nonlinear Analysis: Theory, Methods & Applications, 2014
In 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) \((y_{m})_{m\geq 1}\)
X. Zhong, Wenming Zou
openaire   +3 more sources

A minimization problem with variable growth on Nehari manifold

Monatshefte für Mathematik, 2016
In 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.
openaire   +2 more sources

Ground state solutions for weighted biharmonic Kirchhoff problem via the Nehari manifold approach

Applicable Analysis
In this article, we delve into the investigation of the following non-local problem within the unit ball $ B_1 $ B1 of $ \mathbb {R}^4 $ R4: \[ g\left(\int_{B_{1}}w_{\beta}(x) |\Delta u|^{2}\right)\Delta_{w_{\beta}}^{2}u =|u|^{q-2}u + f(x,u) \ {\rm in ...
Brahim Dridi, Rached Jaidane, Oussama Dammak   +2 more
semanticscholar   +1 more source

The Nehari manifold and application to a semilinear elliptic system

Nonlinear Analysis: Theory, Methods & Applications, 2009
Abstract 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 )
openaire   +2 more sources

The Nehari manifold for the Schrödinger–Poisson systems with steep well potential

Complex Variables and Elliptic Equations, 2018
In 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
openaire   +2 more sources

The Nehari manifold for a semilinear elliptic equation involving a sublinear term

Calculus of Variations and Partial Differential Equations, 2004
The author discusses the problem of existence and multiplicity of non-negative solutions to the problem \[ \begin{cases} -\Delta u(x)=\lambda u(x)+b(x)| u(x)| ^{\gamma-2}u(x)& \text{for }u\in\Omega\\ u(x)=0& \text{for }x\in\partial\Omega,\end{cases}\eqno(1) \] where \(\Omega\subset \mathbb R^N\) is a smooth bounded domain, \(b:\Omega\to \mathbb R\) a ...
openaire   +3 more sources

The Nehari manifold for nonlocal elliptic operators involving concave–convex nonlinearities

Zeitschrift für angewandte Mathematik und Physik, 2014
In 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, Shengbing Deng, Wenjing Chen   +2 more
openaire   +3 more sources

The Nehari Manifold and its Application to a Fractional Boundary Value Problem

Differential Equations and Dynamical Systems, 2013
In 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)
openaire   +2 more sources

The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

Applied Mathematics and Computation, 2012
Abstract 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
openaire   +2 more sources

Non-Nehari manifold method for periodic discrete superlinear Schrödinger equation

Acta Mathematica Sinica, English Series, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources