اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGround States for a nonlinear Schrodinger system with sublinear coupling terms
112
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the existence of ground states for the coupled Schrodinger system begin{equation} left{begin{array}{lll} displaystyle -Delta u_i+lambda_i u_i= mu_i |u_i|^{2q-2}u_i+sum_{j eq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i u_iin H^1(mathbb{R}^n), quad i=1,ldots, d, end{array}right. end{equation} $ngeq 1$, for $lambda_i,mu_i >0$, $b_{ij}=b_{ji}>0$ (the so-called symmetric attractive case) and $1<q<n/(n-2)^+$. We prove the existence of a nonnegative ground state $(u_1^*,ldots,u_d^*)$ with $u_i^*$ radially decreasing. Moreover we show that, for $1<q<2$, such ground states are positive in all dimensions and for all values of the parameters.
قيم البحث
اقرأ أيضاً
We give short survey on the question of asymptotic stability of ground states of nonlinear Schrodinger equations, focusing primarily on the so called nonlinear Fermi Golden Rule.
We consider systems of weakly coupled Schrodinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary c
onditions for a sequence of least energy solutions to concentrate.
We study the nonlinear Schrodinger system [ begin{cases} displaystyle iu_t+Delta u-u+(frac{1}{9}|u|^2+2|w|^2)u+frac{1}{3}overline{u}^2w=0, idisplaystyle sigma w_t+Delta w-mu w+(9|w|^2+2|u|^2)w+frac{1}{9}u^3=0, end{cases} ] for $(x,t)in mathbb{R
}^ntimesmathbb{R}$, $1leq nleq 3$ and $sigma,mu>0$. This system models the interaction between an optical beam and its third harmonic in a material with Kerr-type nonlinear response. We prove the existence of ground state solutions, analyse its stability, and establish local and global well-posedness results as well as several criteria for blow-up.
This article concerns the fractional elliptic equations begin{equation*}(-Delta)^{s}u+lambda V(x)u=f(u), quad uin H^{s}(mathbb{R}^N), end{equation*}where $(-Delta)^{s}$ ($sin (0,,,1)$) denotes the fractional Laplacian, $lambda >0$ is a parameter, $
Vin C(mathbb{R}^N)$ and $V^{-1}(0)$ has nonempty interior. Under some mild assumptions, we establish the existence of nontrivial solutions. Moreover, the concentration of solutions is also explored on the set $V^{-1}(0)$ as $lambdatoinfty$.
We are concerned with the following nonlinear Schrodinger equation $$-varepsilon^2Delta u+ V(x)u=|u|^{p-2}u,~uin H^1(R^N),$$ where $Ngeq 3$, $2<p<frac{2N}{N-2}$. For $varepsilon$ small enough and a class of $V(x)$, we show the uniqueness of positiv
e multi-bump solutions concentrating at $k$ different critical points of $V(x)$ under certain assumptions on asymptotic behavior of $V(x)$ and its first derivatives near those points. The degeneracy of critical points is allowed in this paper.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
