共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we study the nonlinear one-dimensional periodic wave equation with x-dependent coefficients u(x)ytt−(ux(x)yx)+g(x,t,y)=f(x,t) on (0,π)×R under the boundary conditions a1y(0,t)+b1yx(0,t)=0, a2y(π,t)+b2yx(π,t)=0 ( for i=1,2) and the periodic conditions y(x,t+T)=y(x,t), yt(x,t+T)=yt(x,t). Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. A main concept is the notion “weak solution” to be given in Section 2. For T is the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained. 相似文献
2.
Gian-Luigi Forti Justyna Sikorska 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):343-350
We study the stability of the Drygas functional equation:
g(xy)+g(xy−1)=2g(x)+g(y)+g(y−1) 相似文献
3.
Jinghai Shao 《Bulletin des Sciences Mathématiques》2006,130(8):720-738
Let (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton-Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux. 相似文献
4.
In this paper, we study the existence, uniqueness and asymptotic stability of travelling wavefronts of the following equation:
ut(x,t)=D[u(x+1,t)+u(x-1,t)-2u(x,t)]-du(x,t)+b(u(x,t-r)), 相似文献
5.
Jae-Hyeong Bae 《Applied mathematics and computation》2010,216(1):87-307
For each n=1,2,3, we obtain the general solution and the stability of the functional equation
f(2x+y)+f(2x-y)=2n-2[f(x+y)+f(x-y)+6f(x)]. 相似文献
6.
Seshadev Padhi 《Applied mathematics and computation》2010,216(8):2450-2456
This paper is concerned with the existence of three positive T-periodic solutions of the first order functional differential equations of the form
x′(t)=a(t)x(t)-λb(t)f(t,x(h(t))), 相似文献
7.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 相似文献
8.
J.A. MacDougall 《Discrete Mathematics》2008,308(13):2756-2763
An edge-magic total labeling on G is a one-to-one map λ from V(G)∪E(G) onto the integers 1,2,…,|V(G)∪E(G)| with the property that, given any edge (x,y), λ(x)+λ(x,y)+λ(y)=k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V(G)|-3 edges. In this paper we study graphs of this maximum size. 相似文献
9.
In this paper, we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation
x′(t)=α(t)x(t)-β(t)x2(t)+γ(t)x(t-τ(t))x(t). 相似文献
10.
11.
We study the existence of homoclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C1(R×Rn,R), V(t,q)=-K(t,q)+W(t,q) is T-periodic in t. A map K satisfies the “pinching” condition b1|q|2?K(t,q)?b2|q|2, W is superlinear at the infinity and f is sufficiently small in L2(R,Rn). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations. 相似文献
12.
Mouez Dimassi 《Journal of Functional Analysis》2005,225(1):193-228
We study the spectral shift function s(λ,h) and the resonances of the operator P(h)=-Δ+V(x)+W(hx). Here V is a periodic potential, W a decreasing perturbation and h a small positive constant. We give a representation of the derivative of s(λ,h) related to the resonances of P(h), and we obtain a Weyl-type asymptotics of s(λ,h). We establish an upper bound O(h-n+1) for the number of the resonances of P(h) lying in a disk of radius h. 相似文献
13.
Shih Ping Tung 《Journal of Number Theory》2010,130(4):912-929
In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z. 相似文献
14.
This paper studies the scattering matrix S(E;?) of the problem
−?2ψ″(x)+V(x)ψ(x)=Eψ(x) 相似文献
15.
Vladimir Umanskiy 《Advances in Mathematics》2003,180(1):176-186
Given p≠0 and a positive continuous function g, with g(x+T)=g(x), for some 0<T<1 and all real x, it is shown that for suitable choice of a constant C>0 the functional has a minimizer in the class of positive functions u∈C1(R) for which u(x+T)=u(x) for all x∈R. This minimizer is used to prove the existence of a positive periodic solution y∈C2(R) of two-dimensional Lp-Minkowski problem y1−p(x)(y″(x)+y(x))=g(x), where p∉{0,2}. 相似文献
16.
Sin-Ei Takahasi Takeshi Miura Hiroyuki Takagi 《Journal of Mathematical Analysis and Applications》2007,329(2):1191-1203
We give the solution of the functional equation f(x+y)+λf(x)f(y)=Φ(x,y) under some conditions. Also we show its Hyers-Ulam stability. 相似文献
17.
Eliza Jab?ońska 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2465-572
Let X be a separable F-space over the field K of reals or complex numbers. We characterize solutions of the equation
f(x+M(f(x))y)=f(x)f(y) 相似文献
18.
19.
We consider an operator Q(V) of Dirac type with a meromorphic potential given in terms of a function V of the form V(z)=λV1(z)+μV2(z), z∈C?{0}, where V1 is a complex polynomial of 1/z, V2 is a polynomial of z, and λ and μ are nonzero complex parameters. The operator Q(V) acts in the Hilbert space L2(R2;C4)=⊕4L2(R2). The main results we prove include: (i) the (essential) self-adjointness of Q(V); (ii) the pure discreteness of the spectrum of Q(V); (iii) if V1(z)=z−p and 4?degV2?p+2, then kerQ(V)≠{0} and dimkerQ(V) is independent of (λ,μ) and lower order terms of ∂V2/∂z; (iv) a trace formula for dimkerQ(V). 相似文献
20.
Octavian G. Mustafa 《Journal of Mathematical Analysis and Applications》2008,348(1):211-219
We give a constructive proof of existence to oscillatory solutions for the differential equations x″(t)+a(t)λ|x(t)|sign[x(t)]=e(t), where t?t0?1 and λ>1, that decay to 0 when t→+∞ as O(t−μ) for μ>0 as close as desired to the “critical quantity” . For this class of equations, we have limt→+∞E(t)=0, where E(t)<0 and E″(t)=e(t) throughout [t0,+∞). We also establish that for any μ>μ? and any negative-valued E(t)=o(t−μ) as t→+∞ the differential equation has a negative-valued solution decaying to 0 at + ∞ as o(t−μ). In this way, we are not in the reach of any of the developments from the recent paper [C.H. Ou, J.S.W. Wong, Forced oscillation of nth-order functional differential equations, J. Math. Anal. Appl. 262 (2001) 722-732]. 相似文献