Results 21 to 30 of about 299,484 (312)

Normalized solutions of nonlinear Schrödinger equations [PDF]

Archiv der Mathematik, 2012
We consider the problem -Δu - g(u) = λu, u \in H^1(\R^N), \int_{\R^N} u^2 = 1, λ\in\R, in dimension $N\ge2$. Here $g$ is a superlinear, subcritical, possibly nonhomogeneous, odd nonlinearity. We deal with the case where the associated functional is not bounded below on the $L^2$-unit sphere, and we show the existence of infinitely many solutions.
Bartsch, Thomas, de Valeriola, Sébastien   +1 more
openaire   +2 more sources

Normalized solutions to the Schrödinger systems with double critical growth and weakly attractive potentials

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we look for solutions to the following critical Schrödinger system $$\begin{cases} -\Delta u+(V_1+\lambda_1)u=|u|^{2^*-2}u+|u|^{p_1-2}u+\beta r_1|u|^{r_1-2}u|v|^{r_2}&{\rm in}\ \mathbb{R}^N,\\ -\Delta v+(V_2+\lambda_2)v=|v|^{2^*-2}v+|v ...
Lei Long, Xiaojing Feng
doaj   +1 more source

Normalized multi-bump solutions for saturable Schrödinger equations

Advances in Nonlinear Analysis, 2019
In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function:
Wang Xiaoming, Wang Zhi-Qiang
doaj   +1 more source

Existence of normalized solutions for the Schrödinger equation

Communications in Analysis and Mechanics, 2023
In this paper, we devote to studying the existence of normalized solutions for the following Schrödinger equation with Sobolev critical nonlinearities. $ \begin{align*} &\left\{\begin{array}{ll} -\Delta u = \lambda u+\mu\lvert u \rvert^{q-2}u+\
Shengbing Deng, Qiaoran Wu
doaj   +1 more source

Univalence of normalized solutions of W″(z)+p(z)W(z)=0

International Journal of Mathematics and Mathematical Sciences, 1982
Denote solutions of W″(z)+p(z)W(z)=0 by Wα(z)=zα[1+∑n=1∞anzn] and Wβ(z)=zβ[1+∑n=1∞bnzn], where ...
R. K. Brown
doaj   +1 more source

Normalized solutions for the p-Laplacian equation with a trapping potential

Advances in Nonlinear Analysis, 2023
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2.
Wang Chao, Sun Juntao
doaj   +1 more source

A comprehensive review on the existence of normalized solutions for four classes of nonlinear elliptic equations [PDF]

Opuscula Mathematica
This paper provides a comprehensive review of recent results concerning the existence of normalized solutions for four classes of nonlinear elliptic equations: Schrödinger equations, Schrödinger-Poisson equations, Kirchhoff equations, and Choquard ...
Sitong Chen, Xianhua Tang
doaj   +1 more source

Standing waves to upper critical Choquard equation with a local perturbation: Multiplicity, qualitative properties and stability

Advances in Nonlinear Analysis, 2022
In this article, we consider the upper critical Choquard equation with a local perturbation −Δu=λu+(Iα∗∣u∣p)∣u∣p−2u+μ∣u∣q−2u,x∈RN,u∈H1(RN),∫RN∣u∣2=a,\left\{\begin{array}{l}-\Delta u=\lambda u+\left({I}_{\alpha }\ast | u\hspace{-0.25em}{| }^{p})| u\hspace{
Li Xinfu
doaj   +1 more source

Combinatorial solutions to normal ordering of bosons [PDF]

Czechoslovak Journal of Physics, 2005
Presented at 14th Int. Colloquium on Integrable Systems, Prague, Czech Republic, 16-18 June 2005.
Błasiak, P., Gawron, A., Horzela, A., Penson, K. A., Solomon, A. I.   +4 more
openaire   +3 more sources

The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases

Advances in Nonlinear Analysis, 2022
This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P)(−Δ)su+λu=μ∣u∣p−2u+∣u∣2s∗−2u,x∈RN,u>0,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda
Li Quanqing, Zou Wenming
doaj   +1 more source