Results 11 to 20 of about 136,279 (261)
Mathematics, 2022 In this paper, we consider a new kind of Kirchhoff-type equation which is stated in the introduction. Under certain assumptions on potentials, we prove by variational methods that the equation has at least a ground state solution and investigate the ...
Li Zhou, Chuanxi Zhu
doaj +1 more source
On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity
Boundary Value Problems, 2023 In this paper, we consider a class of fractional Choquard equations with indefinite potential ( − Δ ) α u + V ( x ) u = [ ∫ R N M ( ϵ y ) G ( u ) | x − y | μ d y ] M ( ϵ x ) g ( u ) , x ∈ R N , $$ (-\Delta )^{\alpha}u+V(x)u= \biggl[ \int _{{\mathbb{R ...
Fangfang Liao +3 more
doaj +1 more source
Ground state and non-ground state solutions of some strongly coupled elliptic systems [PDF]
Transactions of the American Mathematical Society, 2011 We study an elliptic system of the formLu=|v|p−1vLu = \left | v\right |^{p-1} vandLv=|u|q−1uLv=\left | u\right |^{q-1} uinΩ\Omegawith homogeneous Dirichlet boundary condition, whereLu:=−ΔuLu:=-\Delta uin the case of a bounded domain andLu:=−Δu+uLu:=-\Delta u + uin the cases of an exterior domain or the whole spaceRN\mathbb {R}^N.
Bonheure, Denis +2 more
openaire +1 more source
Ground state solutions for the nonlinear Schrödinger–Maxwell equations
Journal of Mathematical Analysis and Applications, 2008 27 ...
Azzollini, A., POMPONIO, Alessio
openaire +7 more sources
Open Mathematics, 2021 In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R ...
Zhu Yuting +3 more
doaj +1 more source
Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
Advances in Nonlinear Analysis, 2021 This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem.
Pan Jingjing, Zhang Jian
doaj +1 more source
Ground state sign-changing solutions for semilinear Dirichlet problems
Boundary Value Problems, 2018 In the present paper, we consider the existence of ground state sign-changing solutions for the semilinear Dirichlet problem 0.1 {−△u+λu=f(x,u),x∈Ω;u=0,x∈∂Ω, $$ \left \{ \textstyle\begin{array}{l@{\quad}l} -\triangle u+\lambda u=f(x, u), & \hbox{$x\in ...
Xiaoyan Lin, Xianhua Tang
doaj +1 more source
Ground state solutions to a class of critical Schrödinger problem
Advances in Nonlinear Analysis, 2021 We consider the following critical nonlocal Schrödinger problem with general ...
Mao Anmin, Mo Shuai
doaj +1 more source
Ground state solutions for periodic Discrete nonlinear Schrödinger equations
AIMS Mathematics, 2021 <abstract><p>In this paper, we consider the following periodic discrete nonlinear Schrödinger equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} Lu_{n}-\omega u_{n} = g_{n}(u_{n}), \qquad n = (n_{1}, n_{2}, ..., n_{m})\in \mathbb{Z}^{m}, \end{equation*} $\end ...
Xionghui Xu, Jijiang Sun
openaire +2 more sources
Ground state solutions for a quasilinear Kirchhoff type equation
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We study the ground state solutions of the following quasilinear Kirchhoff type equation \[ -\left(1+b\int_{\mathbb{R}^{3}}|\nabla u|^2dx\right)\Delta u + V(x)u-[\Delta(u^2)]u=|u|^{10}u+\mu |u|^{p-1}u,\qquad x\in \mathbb{R}^3, \] where $b\geq 0$ and $\mu$
Hongliang Liu, Haibo Chen, Qizhen Xiao
doaj +1 more source