共查询到20条相似文献,搜索用时 78 毫秒
1.
For α[1,2) we consider operators of the form and for α(0,1) we consider the same operator but where the f term is omitted. We prove, under appropriate conditions on A(x,h), that any solution u to will be in Cα+β if fCβ. 相似文献
2.
Ravi P. Agarwal Donal ORegan Patricia J.Y. Wong 《Mathematical and Computer Modelling》2009,50(7-8):999-1025
We consider the system of Hammerstein integral equations where T>0 is fixed, ρi’s are given functions and the nonlinearities fi(t,x1,x2,…,xn) can be singular at t=0 and xj=0 where j{1,2,,n}. Criteria are offered for the existence of constant-sign solutions, i.e., θiui(t)≥0 for t[0,T] and 1≤i≤n, where θi{1,−1} is fixed. The tools used are a nonlinear alternative of Leray–Schauder type, Krasnosel’skii’s fixed point theorem in a cone and Schauder’s fixed point theorem. We also include examples and applications to illustrate the usefulness of the results obtained. 相似文献
3.
Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings 总被引:1,自引:0,他引:1
Let E be a real reflexive Banach space with uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed and convex subset of E. Let T:K→K be a strictly pseudo-contractive map and let L>0 denote its Lipschitz constant. Assume F(T){xK:Tx=x}≠0/ and let zF(T). Fix δ(0,1) and let δ* be such that δ*δL(0,1). Define , where δn(0,1) and limδn=0. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: . For arbitrary x0,uK, define a sequence {xn}K by xn+1=αnu+(1−αn)Snxn. Then, {xn} converges strongly to a fixed point of T. 相似文献
4.
In this article, the author studies the boundedness and convergence for the {(x) = a(y) - f(x),(y) = b(y)β(x) - g(x) e(t),where a(y), b(y), f(x),g(x),β(x) are real continuous functions in y ∈ R or x ∈ R,β(x) ≥ 0 for all x and e(t) is a real continuous function on R = {t: t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended. 相似文献
5.
In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform H(o)lder condition, and obtain the uniform packing dimension of multiparameter stable processes.If Z is a stable (N, d, α)-process and αN ≤ d, then the following holds with probability 1 Dim Z(E) = α DimE for any Borel setE ∈ B(R N),where Z(E) = {x: (E) t ∈ E, Z(t) = x}. Dim(E) denotes the packing dimension of E. 相似文献
6.
Let G be a graph. For u,vV(G) with distG(u,v)=2, denote JG(u,v)={wNG(u)∩NG(v)|NG(w)NG(u)NG(v){u,v}}. A graph G is called quasi claw-free if JG(u,v)≠ for any u,vV(G) with distG(u,v)=2. In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. In this paper we show that every 4-connected line graph of a quasi claw-free graph is hamiltonian connected. 相似文献
7.
8.
We apply the techniques of monotone and relative rearrangements to the nonrearrangement invariant spaces Lp()(Ω) with variable exponent. In particular, we show that the maps uLp()(Ω)→k(t)u*Lp*()(0,measΩ) and uLp()(Ω)→u*Lp*()(0,measΩ) are locally -Hölderian (u* (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents. 相似文献
9.
This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W=e-Q, which are given as follows. Let an=an(Q) be the nth Mhaskar–Rahmanov–Saff number, φn(x)=max{n-2/3,1-|x|/an}, and d>0. Assume that QC(R) is even, , and for some A,B>1Then for xRand for |x|an(1+dn-2/3) 相似文献
10.
Existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function 总被引:1,自引:0,他引:1
This paper is concerned with the existence, multiplicity and stability of positive solutions of an indefinite weight boundary value problemwhere aC[0,1] changes sign. The proof of our main result is based upon bifurcation techniques. 相似文献
11.
Andreas W.M. Dress Katharina T. Huber Jacobus Koolen Vincent Moulton 《Applied Mathematics Letters》2008,21(6):545-548
In this note, we will define topological and virtual cut points of finite metric spaces and show that, though their definitions seem to look rather distinct, they actually coincide. More specifically, let X denote a finite set, and let denote a metric defined on X. The tight span T(D) of D consists of all maps for which f(x)=supyX(xy−f(x)) holds for all xX. Define a map fT(D) to be a topological cut point of D if T(D)−{f} is disconnected, and define it to be a virtual cut point of D if there exists a bipartition (or split) of the support of f into two non-empty sets A and B such that ab=f(a)+f(b) holds for all points aA and bB. It will be shown that, for any given metric D, topological and virtual cut points actually coincide, i.e., a map fT(D) is a topological cut point of D if and only if it is a virtual cut point of D. 相似文献
12.
Let Lq (1q<∞) be the space of functions f measurable on I=[−1,1] and integrable to the power q, with normL∞ is the space of functions measurable on I with normWe denote by AC the set of all functions absolutely continuous on I. For nN, q[1,∞] we setWn,q={f:f(n−1)AC, f(n)Lq}.In this paper, we consider the problem of accuracy of constants A, B in the inequalities (1) || f(m)||qA|| f||p+B|| f(m+k+1)||r, mN, kW; p,q,r[1,∞], fWm+k+1,r. 相似文献
13.
陈泽乾 《数学物理学报(B辑英文版)》2009,29(5):1225-1232
In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation:
{(-△x+△y)φ(x,y)=0,x,y∈Ω
φ|δΩxδΩ=f
where Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods. 相似文献
{(-△x+△y)φ(x,y)=0,x,y∈Ω
φ|δΩxδΩ=f
where Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods. 相似文献
14.
R 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2008,25(4):659-678
For a nonnegative, uniformly convex HC2(R2) with H(0)=0, if uC(Ω), ΩR2, is a viscosity solution of the Aronsson equation (1.7), then uC1(Ω). This generalizes the C1-regularity theorem on infinity harmonic functions in R2 by Savin [O. Savin, C1-regularity for infinity harmonic functions in dimensions two, Arch. Ration. Mech. Anal. 176 (3) (2005) 351–361] to the Aronsson equation. 相似文献
15.
In this note the following inequality is proved. For any nonnegative measure μH−1(R2), xR2 and 0<r<1, there holds(1) where C is a positive constant. Using (1) an estimate for the vorticity maximal function similar to the estimate in Majda [A. Majda, Remarks on weak solutions for vortex sheets with a distinguished sign, Indiana Univ. Math. J. 42 (1993) 921–939] is established without assuming the initial vorticity having compact support. From this a more simple proof of the Delort's celebrated theorem [J.M. Delort, Existence de mappes de fourbillon en dimension deux, J. Amer. Math. Soc. 4 (1991) 553–586] is presented. 相似文献
16.
Galerkin methods are used to approximate the singular integral equation with solution φ having weak singularity at the endpoint −1, where a, b≠0 are constants. In this case φ is decomposed as φ(x)=(1−x)α(1+x)βu(x), where β=−α, 0<α<1. Jacobi polynomials are used in the discussions. Under the conditions fHμ[−1,1] and k(t,x)Hμ,μ[−1,1]×[−1,1], 0<μ<1, the error estimate under a weighted L2 norm is O(n−μ). Under the strengthened conditions f″Hμ[−1,1] and , 2α−<μ<1, the error estimate under maximum norm is proved to be O(n2α−−μ+), where , >0 is a small enough constant. 相似文献
17.
Juan Luis García Guirao Raquel García Rubio 《Journal of Mathematical Analysis and Applications》2010,362(2):350-354
The aim of the present paper is to study the structure of the nonwandering set of points Ω() for the skew-product maps of the unit square , (x,y)→(f(x),g(x,y)), with base f having closed set of periodic points. For every and every point (x,y) with x periodic of period px by f and y not chain recurrent of Fpx|Ix, where , we prove that (x,y)Ω(F). On the other hand we construct a map with an isolated fixed point x0 of f and y0Ω(F|Ix0) such that (x0,y0)Ω(F0). 相似文献
18.
Konstantin Yu. Osipenko 《Journal of Approximation Theory》1999,97(2):384
LetSβ{z
: |Im z|<β}. For 2π-periodic functions which are analytic inSβwithp-integrable boundary values, we construct an optimal method of recovery off′(ξ), ξSβ, using information about the valuesf(x1), mldr;, f(xn), xj[0, 2π). 相似文献
19.
Let Ω be a bounded domain with smooth boundary in . For the more general weight b, some nonlinearities f and singularities g, by two kinds of nonlinear transformations, a new perturbation method, which was introduced by García Melián in [J. García Melián, Boundary behavior of large solutions to elliptic equations with singular weights, Nonlinear Anal. 67 (2007) 818–826], and comparison principles, we show that the boundary behavior of solutions to a boundary blow-up elliptic problem Δw=b(x)f(w),w>0,xΩ,w|∂Ω=∞ and a singular Dirichlet problem −Δu=b(x)g(u),u>0,xΩ,u|∂Ω=0 has the same form under the nonlinear transformations, which can be determined in terms of the inverses of the transformations. 相似文献
20.
Igor E. Zverovich 《Journal of Algorithms in Cognition, Informatics and Logic》2006,58(2):118-133
A proper k-coloring C1,C2,…,Ck of a graph G is called strong if, for every vertex uV(G), there exists an index i{1,2,…,k} such that u is adjacent to every vertex of Ci. We consider classes of strongly k-colorable graphs and show that the recognition problem of is NP-complete for every k4, but it is polynomial-time solvable for k=3. We give a characterization of in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring. 相似文献