Results 1 to 10 of about 2,064,106 (289)

Ground states for a coupled Schrödinger system with general nonlinearities

Boundary Value Problems, 2020
We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings.
Xueliang Duan, Gongming Wei, Haitao Yang
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Ground State Solutions for Kirchhoff Type Quasilinear Equations

Advanced Nonlinear Studies, 2018
Abstract In this paper, we are concerned with quasilinear equations of Kirchhoff type, and prove the existence of ground state signed solutions and sign-changing solutions by using the Nehari method.
Liu Xiangqing, Zhao Junfang
openaire   +3 more sources

Fractional p&q-Laplacian problems with potentials vanishing at infinity [PDF]

Opuscula Mathematica, 2020
In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional \(p\&q\)-Laplacian problems \[\begin{aligned} (-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(
Teresa Isernia
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Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we study Kirchhoff equations with logarithmic nonlinearity: \begin{equation*} \begin{cases} -(a+b\int_\Omega|\nabla u|^2)\Delta u+ V(x)u=|u|^{p-2}u\ln u^2, & \mbox{in}\ \Omega,\\ u=0,& \mbox{on}\ \partial\Omega, \end{cases} \end{equation*}
Lixi Wen, Xianhua Tang, Sitong Chen
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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
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Multiple positive solutions for nonlinear coupled fractional Laplacian system with critical exponent

Boundary Value Problems, 2018
In this paper, we study the following critical system with fractional Laplacian: {(−Δ)su+λ1u=μ1|u|2∗−2u+αγ2∗|u|α−2u|v|βin Ω,(−Δ)sv+λ2v=μ2|v|2∗−2v+βγ2∗|u|α|v|β−2vin Ω,u=v=0in RN∖Ω, $$\textstyle\begin{cases} (-\Delta)^{s}u+\lambda_{1}u=\mu_{1}|u|^{2^{\ast}-
Maoding Zhen, Jinchun He, Haoyuan Xu, Meihua Yang   +3 more
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Ground-state Properties of Small-Size Nonlinear Dynamical Lattices [PDF]

, 2006
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of ...
A. Vezzani, M. W. Jack, P. Buonsante, P. G. Kevrekidis, R. Franzosi, V. Penna, Yu. S. Kivshar   +6 more
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Comment on "Superfluid stability in the BEC-BCS crossover" [PDF]

, 2007
We point out an error in recent work by Pao, Wu, and Yip [Phys. Rev.B {\bf 73}, 132506 (2006)], that stems from their use of a necessary but not sufficient condition [positive compressibility (magnetic susceptibility) and superfluid stiffness] for the ...
Radzihovsky, Leo, Sheehy, Daniel E.
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Ground state solutions for quasilinear Schrödinger systems

Journal of Mathematical Analysis and Applications, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Yuxia, Tang, Zhongwei
openaire   +2 more sources

Existence of sign-changing solution with least energy for a class of Kirchhoff-type equation in $\mathbb{R}^N$

Electronic Journal of Qualitative Theory of Differential Equations, 2017
We consider the existence of least energy sign-changing (nodal) solution of Kirchhoff-type elliptic problems with general nonlinearity. Using a truncated technique and constrained minimization on the nodal Nehari manifold, we obtain that the Kirchhoff ...
Xianzhong Yao, Chunlai Mu
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