Results 21 to 30 of about 1,045,959 (290)
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 +1 more
openaire +2 more sources
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
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Effective-Mass Klein-Gordon-Yukawa Problem for Bound and Scattering States [PDF]
, 2011 Bound and scattering state solutions of the effective-mass Klein-Gordon equation are obtained for the Yukawa potential with any angular momentum $\ell$.
Abramowitz M. +3 more
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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
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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
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Exact solutions of the radial Schrodinger equation for some physical potentials [PDF]
, 2007 By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions.
A. Chatterjee +42 more
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A comprehensive review on the existence of normalized solutions for four classes of nonlinear elliptic equations [PDF]
Opuscula MathematicaThis 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
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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
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Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation
Advances in Nonlinear Analysis, 2023 In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: (−Δ)su=λu+α(Iμ*∣u∣q)∣u∣q−2u+(Iμ*∣u∣2μ,s*)∣u∣2μ,s*−2u,inRN,{\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u|
Lan Jiali, He Xiaoming, Meng Yuxi
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On finite-difference approximations for normalized Bellman equations [PDF]
, 2009 A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of ...
A.N. Shiryaev +18 more
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