Results 31 to 40 of about 317,499 (205)

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
openalex   +5 more sources

On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent

Journal of Function Spaces, 2022
In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
doaj   +2 more sources

Critical Fractional p-Laplacian System with Negative Exponents

Journal of Function Spaces, 2023
In this paper, we consider a class of fractional p-Laplacian problems with critical and negative exponents. By decomposition of the Nehari manifold, the existence and multiplicity of nontrivial solutions for the above problems are established with ...
Qinghao Zhu, Jianming Qi
doaj   +2 more sources

Existence of solutions for singular double phase problems via the Nehari manifold method [PDF]

Analysis and Mathematical Physics, 2022
AbstractIn this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has the combined effect of a singular and of a parametric term. Based on the fibering method by using the Nehari manifold we are going to prove the existence of at least two weak solutions for such problems when the parameter is
Wulong Liu, Guowei Dai, Nikolaos S. Papageorgiou, Patrick Winkert   +3 more
openaire   +4 more sources

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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Systems of coupled Schrödinger equations with sign-changing nonlinearities via classical Nehari manifold approach [PDF]

Complex Var. Elliptic Equ., Vol. 64, Issue 7 (2019), p. 1237-1256, 2018
We propose existence and multiplicity results for the system of Schr\"odinger equations with sign-changing nonlinearities in bounded domains or in the whole space $\mathbb{R}^N$. In the bounded domain we utilize the classical approach via the Nehari manifold, which is (under our assumptions) a differentiable manifold of class $\mathcal{C}^1$ and the ...
Bartosz Bieganowski
arxiv   +3 more sources

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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Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

International Journal of Differential Equations
This paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent.
Mohammed El Mokhtar Ould El Mokhtar, Saleh Fahad Aljurbua   +1 more
doaj   +2 more sources

The Nehari manifold for elliptic equation involving the square root of the Laplacian

Journal of Differential Equations, 2011
AbstractIn this paper, we introduce the Nehari manifold for elliptic problems involving the square root of the Laplacian. We use it to establish the existence of solutions and multiple solutions for some nonlinear elliptic problem with sign-changing weight. We also establish some bifurcation results and non-existence results.
Xiaohui Yu
openalex   +3 more sources

The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition

Journal of Mathematical Analysis and Applications, 2012
Abstract Using the Nehari manifold and fibering maps, we prove the existence theorem of the nonlinear boundary problem − Δ u + u = | u | p − 2 u for x ∈ Ω ; ∂ u ∂ n = λ | u | q − 2 u for x ∈ ∂ Ω on a bounded domain Ω ⊆ R N .
Jinguo Zhang, Xiaochun Liu
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