共查询到20条相似文献,搜索用时 0 毫秒
1.
《数学物理学报(B辑英文版)》2017,37(2):555-572
In this article, we study the following nonhomogeneous Schr¨odinger-Poisson equations -?u + λV(x)u + K(x)φu = f(x, u) + g(x), x ∈ R~3,?-?φ = K(x)u~2, x ∈ R~3,where λ 0 is a parameter. Under some suitable assumptions on V, K, f and g, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. In particular, the potential V is allowed to be signchanging. 相似文献
2.
刘忠原 《数学物理学报(B辑英文版)》2021,(2):493-504
In this paper, we construct sign-changing radial solutions for a class of Schr?dinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer k, by using a minimization argument, we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda’s theorem, that the minimizer is the desired solution. 相似文献
3.
《数学物理学报(B辑英文版)》2017,(6)
In this paper,we study the following generalized quasilinear Schrdinger equations with critical or supercritical growths-div(g~2(u)▽u) + g(u)g′(u)|▽u|~2+ V(x)u = f(x,u) + λ|u|~(p-2)u,x∈R~N,where λ0,N≥3,g:R → R~+ is a C~1 even function,g(0) = 1,g′(s) ≥ 0 for all s ≥ 0,lim_(|s|→+∞)g(s)/|s|~(α-1):= β 0 for some α≥ 1 and(α-1)g(s) g′(s)s for all s 0 and p ≥α2*.Under some suitable conditions,we prove that the equation has a nontrivial solution for smallλ 0 using a change of variables and variational method. 相似文献
4.
We consider the following nonlinear Schr¨odinger equations -ε2△u + u = Q(x)|u|p-2u in RN, u ∈ H1(RN),where ε is a small positive parameter, N ≥ 2, 2 p ∞ for N = 2 and 2 p 2N/N-2 for N ≥ 3. We prove that this problem has sign-changing(nodal) semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q(x).Moreover, the number of this type of solutions will go to infinity as ε→ 0+. 相似文献
5.
《数学物理学报(B辑英文版)》2020,(1)
In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth (-?)_A~su + V(x)u = |u|~(2_s~*-2) u + λf(x, |u|~2)u, x ∈ R~N,where(-?)_A~s is the fractional magnetic operator with 0 s 1, N 2s, λ 0, 2_s~*=2N/(N-2s),f is a continuous function, V ∈ C(R~N, R) and A ∈ C(R~N, R~N) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method. 相似文献
6.
ONINITIAL BOUNDARYVALUEPROBLEMSFORNONLINEARSCHRDINGEREQUATIONS¥LiYongsheng(李用声)ChenQingyi(陈庆益)(Dept.ofMath.,HuazhongUnv.ofSci... 相似文献
7.
《高校应用数学学报(英文版)》1999,(1)
§1IntroductionMuchatentionhasbeendevotedtothenonlinearSchrodingerequations[1~3].Thisbe-causemanyphysicalphenomenacanbedescrib... 相似文献
8.
TRAVELING WAVE SOLUTIONS AND THEIR STABILITY OF NONLINEAR SCHRDINGER EQUATION WITH WEAK DISSIPATION
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In this paper,several new constant-amplitude and variable-amplitude wave solutions(namely,traveling wave solutions) of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique. 相似文献
9.
In this paper,we study the following Schrodinger-Poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlinearity f is super-cubic,subcritical and that the potential V(x) has a potential well. 相似文献
10.
郭柏灵 《数学物理学报(B辑英文版)》1989,(1)
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term. 相似文献
11.
Yao Zheng'an 《数学物理学报(B辑英文版)》2001,21(1):137-144
1 IntroductionIn this paPer, we collsider the initial and boundaxy value probIem of linear and sentilillearScl1r5dinger equation as fOllows:l ie(x):5:i".,'<">"'>.'<",,'>,"=' 1:!\:?0t:)t>, (l1)wllere E > 0, fl C RN is a bounded open dolllain and T is an ar… 相似文献
12.
The importance of the inverse scattering problem for the Schrdinger equation with energy-dependent potential: 相似文献
13.
The importance of the inverse scattering problem for the Schrdinger equation with energy-dependent potential: has been noticed by quite a few authors. Jaulent and Miodek have used it to solve some nonlinear evolution equations with isospectral condition ξ_t=0. Li and Zhuang have further made use of (1) to expand the solvable class of nonlinear evolution equations. Several physical problems in absorption media can be reduced to the inverse scattoring problem of(1) (see [4]). 相似文献
14.
In this paper, we study the Schr?dinger equations (-?)su + V(x)u = a(x)|u|p-2u + b(x)|u|q-2u, x∈RN,where 0 < s < 1, 2 < q < p < 2s*, 2s* is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods. 相似文献
15.
万优艳 《数学物理学报(B辑英文版)》2010,(4):1199-1218
We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in RN . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function. 相似文献
16.
《数学物理学报(B辑英文版)》2016,(1)
In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear Schr¨odinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter. 相似文献
17.
This paper studies the following semilinear Schrodinger problem It is proven that there exists a bifurcation branch of solutions for the above problem, when g(x) can possibly vanish except for a bounded domain Ω RN. 相似文献
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19.
陈韵梅 《数学物理学报(B辑英文版)》1986,(4)
In this paper we discuss the global existence or blow up of the solution of the following initial boundary value problem for the nonlinear Schrdinger equation 相似文献
20.
By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x=Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained. 相似文献