共查询到20条相似文献,搜索用时 39 毫秒
1.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2009,349(2):436-442
Consider the eigenvalue problem : −Δu=λf(x,u) in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN. Denote by the set of all Carathéodory functions f:Ω×R→R such that for a.e. x∈Ω, f(x,⋅) is Lipschitzian with Lipschitz constant L, f(x,0)=0 and , and denote by (resp. ) the set of λ>0 such that has at least one nonzero classical (resp. weak) solution. Let λ1 be the first eigenvalue for the Laplacian-Dirichlet problem. We prove that and . Our result is a positive answer to Ricceri's conjecture if use f(x,u) instead of f(u) in the conjecture. 相似文献
2.
3.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
4.
Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,308(2):532-540
By constructing the comparison functions and the perturbed method, it is showed that any solution u∈C2(Ω) to the semilinear elliptic problems Δu=k(x)g(u), x∈Ω, u|∂Ω=+∞ satisfies , where Ω is a bounded domain with smooth boundary in RN; , −2<σ, c0>0, ; g∈C1[0,∞), g?0 and is increasing on (0,∞), there exists ρ>0 such that , ∀ξ>0, , . 相似文献
5.
By Karamata regular varying theory, a perturbed argument and constructing comparison functions, we show the exact asymptotic behaviour of the unique solution near the boundary to a singular Dirichlet problem −Δu=b(x)g(u)+λf(u), u>0, x∈Ω, u|∂Ω=0, which is independent on λf(u), and we also show the existence and uniqueness of solutions to the problem, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1((0,∞),(0,∞)) and there exists γ>1 such that , ∀ξ>0, , the function is decreasing on (0,∞) for some s0>0, and b is nonnegative nontrivial on Ω, which may be vanishing on the boundary. 相似文献
6.
Beyza Caliskan Aslan Shari Moskow 《Journal of Mathematical Analysis and Applications》2008,341(2):1028-1041
The following generalized eigenproblem is analyzed: Find , u≠0, and λ∈R such that
D〈∇u,∇v〉=λΩ〈∇u,∇v〉 相似文献
7.
Mahamadi Warma 《Journal of Mathematical Analysis and Applications》2007,336(2):1132-1148
Let Ω⊂RN be a bounded domain with Lipschitz boundary, with a>0 on . Let σ be the restriction to ∂Ω of the (N−1)-dimensional Hausdorff measure and let be σ-measurable in the first variable and assume that for σ-a.e. x∈∂Ω, B(x,⋅) is a proper, convex, lower semicontinuous functional. We prove in the first part that for every p∈(1,∞), the operator Ap:=div(a|∇u|p−2∇u) with nonlinear Wentzell-Robin type boundary conditions
8.
Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
9.
Yuan Zhou 《Journal of Mathematical Analysis and Applications》2011,382(2):577-593
The author establishes some geometric criteria for a Haj?asz-Sobolev -extension (resp. -imbedding) domain of Rn with n?2, s∈(0,1] and p∈[n/s,∞] (resp. p∈(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α∈(0,1) if and only if for some/all s∈[α,1) and p=(2−α)/(s−α), where denotes the restriction of the Triebel-Lizorkin space on Ω. 相似文献
10.
Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,312(1):33-43
By Karamata regular variation theory and constructing comparison functions, we show the exact asymptotic behaviour of the unique classical solution near the boundary to a singular Dirichlet problem −Δu=k(x)g(u), u>0, x∈Ω, u|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN; g∈C1((0,∞),(0,∞)), , for each ξ>0, for some γ>0; and for some α∈(0,1), is nonnegative on Ω, which is also singular near the boundary. 相似文献
11.
Sergiu Aizicovici Veli-Matti Hokkanen 《Journal of Mathematical Analysis and Applications》2004,292(2):540-557
The solvability of the evolution system v′(t)+B(t)u(t)∋f(t), v(t)∈A(t)u(t), 0<t<T, with the periodic condition v(0)=v(T) is investigated in the case where are bounded, possibly degenerate, subdifferentials and are unbounded subdifferentials. 相似文献
12.
Nadejda E. Dyakevich 《Journal of Mathematical Analysis and Applications》2008,338(2):892-901
Let q?0, p?0, T?∞, D=(0,a), , Ω=D×(0,T), and Lu=xqut−uxx. This article considers the following degenerate semilinear parabolic initial-boundary value problem,
13.
For a bounded domain Ω in , N?2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Luλ=λg(x,t,uλ) in , uλ=0 on . We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. satisfying some integrability conditions in (x,t) and
14.
Xuanhao Ding 《Journal of Mathematical Analysis and Applications》2005,309(2):650-660
In this paper we completely characterize the isometries of Bergman space (0?p<∞, p≠2) of bounded symmetric domains. We also prove that a pair of Toeplitz operators Tf and Tg on (0<p<∞, p≠2) is isometric equivalence if and only if there is a τ∈Aut(Ω), such that g=f○τ, where Aut(Ω) is the automorphism group of Ω. 相似文献
15.
Let D be nonempty open convex subset of a real Banach space E. Let be a continuous pseudocontractive mapping satisfying the weakly inward condition and let be fixed. Then for each t∈(0,1) there exists satisfying yt∈tTyt+(1−t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1−. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian. 相似文献
16.
G. Metafune 《Journal of Mathematical Analysis and Applications》2004,294(2):596-613
We deal with Markov semigroups Tt corresponding to second order elliptic operators Au=Δu+〈Du,F〉, where F is an unbounded locally Lipschitz vector field on . We obtain new conditions on F under which Tt is not analytic in . In particular, we prove that the one-dimensional operator Au=u″−x3u′, with domain , , is not sectorial in . Under suitable hypotheses on the growth of F, we introduce a class of non-analytic Markov semigroups in , where μ is an invariant measure for Tt. 相似文献
17.
Alexander Gladkov Kwang Ik Kim 《Journal of Mathematical Analysis and Applications》2008,338(1):264-273
In this paper, we consider a semilinear heat equation ut=Δu+c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition and nonnegative initial data where p>0 and l>0. We prove global existence theorem for max(p,l)?1. Some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given. 相似文献
18.
Markus Biegert 《Journal of Mathematical Analysis and Applications》2009,358(2):294-306
The purpose of this article is to define a capacity on certain topological measure spaces X with respect to certain function spaces V consisting of measurable functions. In this general theory we will not fix the space V but we emphasize that V can be the classical Sobolev space W1,p(Ω), the classical Orlicz-Sobolev space W1,Φ(Ω), the Haj?asz-Sobolev space M1,p(Ω), the Musielak-Orlicz-Sobolev space (or generalized Orlicz-Sobolev space) and many other spaces. Of particular interest is the space given as the closure of in W1,p(Ω). In this case every function u∈V (a priori defined only on Ω) has a trace on the boundary ∂Ω which is unique up to a Capp,Ω-polar set. 相似文献
19.
Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2011,381(2):922-934
In this paper we analyze the second expansion of the unique solution near the boundary to the singular Dirichlet problem −Δu=b(x)g(u), u>0, x∈Ω, u|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN, g∈C1((0,∞),(0,∞)), g is decreasing on (0,∞) with and g is normalised regularly varying at zero with index −γ (γ>1), , is positive in Ω, may be vanishing on the boundary. 相似文献
20.
Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm and be a nonexpansive mapping with F(T):={x∈K:Tx=x}≠∅. For a fixed δ∈(0,1), define by Sx:=(1−δ)x+δTx, ∀x∈K. Assume that {zt} converges strongly to a fixed point z of T as t→0, where zt is the unique element of K which satisfies zt=tu+(1−t)Tzt for arbitrary u∈K. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: ; . For arbitrary x0∈K, let the sequence {xn} be defined iteratively by
xn+1=αnu+(1−αn)Sxn. 相似文献