共查询到20条相似文献,搜索用时 484 毫秒
1.
2.
In this paper, the authors study the equation ut=div(|Du|p−2Du)+|u|q−1u−λl|Du| in RN with p>2. We first prove that for 1?l?p−1, the solution exists at least for a short time; then for , the existence and nonexistence of global (in time) solutions are studied in various situations. 相似文献
3.
In this paper, we consider one-dimensional nonlinear Schrödinger equation iut−uxx+V(x)u+f(2|u|)u=0 on [0,π]×R under the boundary conditions a1u(t,0)−b1ux(t,0)=0, a2u(t,π)+b2ux(t,π)=0, , for i=1,2. It is proved that for a prescribed and analytic positive potential V(x), the above equation admits small-amplitude quasi-periodic solutions corresponding to d-dimensional invariant tori of the associated infinite-dimensional dynamical system. 相似文献
4.
V. Raghavendra 《Journal of Mathematical Analysis and Applications》2003,288(1):314-325
In this paper we study the existence of nontrivial solution of the problem −Δpu−(μ/[d(x)]p)|u|p−2u=f(u) in Ω and u=0 on ∂Ω, where is a bounded domain with smooth boundary in Existence is established using mountain-pass lemma and concentration of compactness principle. 相似文献
5.
We study global existence of solutions for the Cauchy problem of the nonlinear Schrödinger equation iut+Δu=|u|2mu in the 2 dimension case, where m is a positive integer, m?2. Using the high-low frequency decomposition method, we prove that if then for any initial value φ∈Hs(R2), the Cauchy problem has a global solution in C(R,Hs(R2)), and it can be split into u(t)=eitΔφ+y(t), with y∈C(R,H1(R2)) satisfying , where ? is an arbitrary sufficiently small positive number. 相似文献
6.
Tahl Nowik 《Topology and its Applications》2007,154(9):1881-1893
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R3, with values in any Abelian group. We show they are all functions of a universal order 1 invariant which we construct as T⊕P⊕Q, where T is a Z valued invariant reflecting the number of triple points of the immersion, and P,Q are Z/2 valued invariants characterized by the property that for any regularly homotopic immersions , P(i)−P(j)∈Z/2 (respectively, Q(i)−Q(j)∈Z/2) is the number mod 2 of tangency points (respectively, quadruple points) occurring in any generic regular homotopy between i and j.For immersion and diffeomorphism such that i and i○h are regularly homotopic we show:
P(i○h)−P(i)=Q(i○h)−Q(i)=(rank(h∗−Id)+ε(deth∗∗))mod2 相似文献
7.
Let V(x) be a non-negative, bounded potential in RN, N?3 and p supercritical, . We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu−V(x)u+up=0 in RN, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(−2|x|) as |x|→+∞, then for N?4 and this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|x|−μ) with μ>N, then this result still holds provided that N?3 and . Other conditions for solvability, involving behavior of V at ∞, are also provided. 相似文献
8.
We study the following complex Ginzburg-Landau equation with cubic nonlinearity on for under initial and Dirichlet boundary conditions u(x,0)=h(x) for x∈Ω, u(x,t)=Q(x,t) on ∂Ω where h,Q are given smooth functions. Under suitable conditions, we prove the existence of a global solution in H1. Further, this solution approaches to the solution of the NLS limit under identical initial and boundary data as a,b→0+. 相似文献
9.
10.
11.
The existence of a -global attractor is proved for the p-Laplacian equation ut−div(|∇u|p−2∇u)+f(u)=g on a bounded domain Ω⊂Rn(n?3) with Dirichlet boundary condition, where p?2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c1q|u|−k?f(u)u?c2q|u|+k and f′(u)?−l, where q?2 is arbitrary. There is no other restriction on p and q. The asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method, called asymptotic a priori estimate. 相似文献
12.
13.
Positive periodic solutions of functional differential equations 总被引:1,自引:0,他引:1
Haiyan Wang 《Journal of Differential Equations》2004,202(2):354-366
We consider the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x(t)−λb(t)f(x(t−τ(t))), where are ω-periodic, , , f,g∈C([0,∞),[0,∞)), and f(u)>0 for u>0, g(x) is bounded, τ(t) is a continuous ω-periodic function. Define , , i0=number of zeros in the set and i∞=number of infinities in the set . We show that the equation has i0 or i∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively. 相似文献
14.
D.S. Lubinsky 《Journal of Mathematical Analysis and Applications》2006,314(1):266-285
We obtain the rate of growth of the largest eigenvalues and Euclidean condition numbers of the Hankel matrices for a general class of even exponential weights W2=exp(−2Q) on an interval I. As particular examples, we discuss Q(x)=α|x| on I=R, and Q(x)=(d2−x2)−α on I=[−d,d]. 相似文献
15.
16.
Removable singularity of the polyharmonic equation 总被引:1,自引:0,他引:1
Shu-Yu Hsu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):624-627
Let x0∈Ω⊂Rn, n≥2, be a domain and let m≥2. We will prove that a solution u of the polyharmonic equation Δmu=0 in Ω?{x0} has a removable singularity at x0 if and only if as |x−x0|→0 for n≥3 and as |x−x0|→0 for n=2. For m≥2 we will also prove that u has a removable singularity at x0 if |u(x)|=o(|x−x0|2m−n) as |x−x0|→0 for n≥3 and |u(x)|=o(|x−x0|2m−2log(|x−x0|−1)) as |x−x0|→0 for n=2. 相似文献
17.
Zuodong Yang 《Journal of Mathematical Analysis and Applications》2003,288(2):768-783
We show the existence of entire explosive positive radial solutions for quasilinear elliptic systems div(|∇u|m−2∇u)=p(|x|)g(v), div(|∇v|n−2∇v)=q(|x|)f(u) on , where f and g are positive and non-decreasing functions on (0,∞) satisfying the Keller-Osserman condition. 相似文献
18.
Qingye Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):894-903
In this paper we study the existence of infinitely many homoclinic solutions for second order Hamiltonian systems , , where L(t) is unnecessarily positive definite for all t∈R, and W(t,u) is of subquadratic growth as |u|→∞. 相似文献
19.
The paper is concerned with the delay differential equation u″+λb(t)f(u(t−τ))=0 satisfying u(t)=0 for −τ?t?0 and , where denotes the Riemann-Stieltjes integral. By applying the fixed point theorem in cones, we show the relationship between the asymptotic behaviors of the quotient (at zero and infinity) and the open intervals (eigenvalue intervals) of the parameter λ such that the problem has zero, one and two positive solution(s). If g(t)=t, by using a property of the Riemann-Stieltjes integral, the above nonlocal boundary value problem educes a three-point boundary value problem with delay, for which some similar results are established. 相似文献
20.
Under a suitable condition on n and p, the quasilinear equation at critical growth −Δpu=λ|u|p−2u+|u|p∗−2u is shown to admit a nontrivial weak solution for any λ?λ1. Nonstandard linking structures, for the associated functional, are recognized. 相似文献