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THE ABUSE OF NORMAL SALT SOLUTION [PDF]
Journal of the American Medical Association, 1914 The presence of a relatively large proportion of sodium chlorid in our bodies harks back to the composition of sea-water at the time when our ancestors were ameboid inhabitants of the primeval ocean. To a certain amount of sodium chlorid our organisms are habituated, and that amount has become essential to our well-being; larger amounts, however, are ...
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Normal solutions of the Beltrami equation
Journal of Mathematical Analysis and Applications, 1987 A homeomorphism f is said to be quasiconformal, with given complex dilatation μ, in a domain G of the complex plane, if it satisfies the Beltrami equation fz, = μfz, (1) where μ =μ(z) is a complex-valued measurable function on G with μ< k< 1, and fz=1/2(fx-ify), fz = 1/2(fx + ify).
W.R Derrick, Joseph A. Cima
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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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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
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Normalized solutions for the Schrödinger-Poisson system with doubly critical growth
Topological Methods in Nonlinear Analysis, 2023 In this paper we are concerned with normalized solutions to the Schrödinger-Poisson system with doubly critical growth \[ \begin{cases} -\Delta u-\phi |u|^3u=\lambda u+\mu|u|^{q-2}u+|u|^4u, &x \in \R^{3},\\ -\Delta \phi=|u|^5, &x \in \R^{3}, \end{cases}
Yuxi Meng, Xiaoming He
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Normalized solutions for a coupled Schrödinger system [PDF]
Mathematische Annalen, 2020 27 pages, 1 ...
Xuexiu Zhong +2 more
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Normalized concentrating solutions to nonlinear elliptic problems [PDF]
Journal of Differential Equations, 2021 We prove the existence of solutions $( , v)\in \mathbb{R}\times H^{1}( )$ of the elliptic problem \[ \begin{cases} - v+(V(x)+ ) v =v^{p}\ &\text{ in $ , $} \ v>0,\qquad \int_ v^2\,dx = . \end{cases} \] Any $v$ solving such problem (for some $ $) is called a normalized solution, where the normalization is settled in $L^2( )$.
BENEDETTA PELLACCI +3 more
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Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity
Advanced Nonlinear Studies, 2022 In the present paper, we study the existence of the normalized solutions for the following coupled elliptic system with quadratic nonlinearity −Δu−λ1u=μ1∣u∣u+βuvinRN,−Δv−λ2v=μ2∣v∣v+β2u2inRN,\left\{\begin{array}{ll}-\Delta u-{\lambda }_{1}u={\mu }_{1}| u|
Wang Jun, Wang Xuan, Wei Song
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Normalized solution to coupled nonhomogeneous nonlinear elliptic system with three wave interaction under unbounded potentials [PDF]
arXiv, 2022 In this paper, we use the variational method to find the normalized solutions of the quadratic coupled three wave Schrodinger equation with asymmetric coercive potential. We prove the existence of solutions for the system with 2-norm constraints.
arxiv
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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