共查询到20条相似文献,搜索用时 15 毫秒
1.
Let be a function satisfying Carathéodory's conditions and (1−t)e(t)∈L1(0,1). Let ξi∈(0,1), ai∈R, i=1,…,m−2, 0<ξ1<ξ2<?<ξm−2<1 be given. This paper is concerned with the problem of existence of a C1[0,1) solution for the m-point boundary value problem
2.
M. García-Huidobro 《Journal of Mathematical Analysis and Applications》2007,333(1):247-264
Let ? and θ be two increasing homeomorphisms from R onto R with ?(0)=0, θ(0)=0. Let be a function satisfying Carathéodory's conditions, and for each i, i=1,2,…,m−2, let , be a continuous function, with , ξi∈(0,1), 0<ξ1<ξ2<?<ξm−2<1.In this paper we first prove a suitable continuation lemma of Leray-Schauder type which we use to obtain several existence results for the m-point boundary value problem:
3.
Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ1(t) be the unique solution of the linear boundary value problem
u″(t)+a(t)u′(t)+b(t)u(t)=0,t∈(0,1),u(0)=0,u(1)=1. 相似文献
4.
Rehana Bari 《Journal of Mathematical Analysis and Applications》2004,292(1):17-22
For any integer m?2, we consider the 2mth order boundary value problem
(−1)mu(2m)(x)=λg(u(x))u(x),x∈(−1,1), 相似文献
5.
This paper is concerned with the following fourth-order m-point nonhomogeneous boundary value problem $$\begin{array}{l}u^{(4)}(t)=f(t,u(t),u^{\prime \prime }(t)),\quad 0<t<1,\\[3pt]u(0)=u(1)=u^{\prime \prime }(0)=0,\\[3pt]u^{\prime \prime }(1)-\displaystyle\sum_{i=1}^{m-2}a_{i}u^{\prime\prime }(\xi _{i})=-\lambda ,\end{array}$$ where a i ≥0 (i=1,2,…,m?2), 0<ξ1<ξ2<???<ξ m?2<1 and ∑ i=1 m?2 a i ξ i <1, and λ>0 is a parameter. The existence and nonexistence of positive solution are discussed for suitable λ>0 when f is superlinear or sublinear. The main tool used is the well-known Guo-Krasnoselskii fixed point theorem. 相似文献
6.
N. Nyamoradi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(4):145-157
The paper studies the problem of existence of positive solution to the following boundary value problem: $D_{0^ + }^\sigma u''(t) - g(t)f(u(t)) = 0$ , t ∈ (0, 1), u″(0) = u″(1) = 0, au(0) ? bu′(0) = Σ i=1 m?2 a i u(ξ i ), cu(1) + du′(1) = Σ i=1 m?2 b i u(ξ i ), where $D_{0^ + }^\sigma$ is the Riemann-Liouville fractional derivative of order 1 < σ ≤ 2 and f is a lower semi-continuous function. Using Krasnoselskii’s fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is established. 相似文献
7.
Stevo Stevi? 《Applied mathematics and computation》2010,216(1):179-5018
Suppose r∈(0,1],m∈N and 1?k1<k2<?<k2m+1, and let S2m+1={1,2,…,2m+1}. We show that every positive solution to the difference equation
8.
Paco Villarroya 《Journal of Mathematical Analysis and Applications》2011,382(2):534-548
Let m(ξ,η) be a measurable locally bounded function defined in R2. Let 1?p1,q1,p2,q2<∞ such that pi=1 implies qi=∞. Let also 0<p3,q3<∞ and 1/p=1/p1+1/p2−1/p3. We prove the following transference result: the operator
9.
In this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplacian $$(\phi_{p}(u'))'+f(t,u,u')=0,\quad t\in [0,1],$$ subject to the boundary value conditions: $$u'(0)=\sum_{i=1}^{n-2}\alpha_{i}u'(\xi_{i}),\qquad u(1)=\sum_{i=1}^{n-2}\beta_{i}u(\xi_{i}),$$ where φ p (s)=|s| p?2?s,p>1;ξ i ∈(0,1) with 0<ξ 1<ξ 2<???<ξ n?2<1 and α i ,β i satisfy α i ,β i ∈[0,∞),0≤∑ i=1 n?2 α i <1 and 0≤∑ i=1 n?2 β i <1. Using a fixed point theorem for operators in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. 相似文献
10.
Kazushi Yoshitomi 《Indagationes Mathematicae》2005,16(2):289-299
Let q ∈ {2, 3} and let 0 = s0 < s1 < … < sq = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set lj = sj − sj−1 for j ∈ 1, q. Given (p1,, pq) ∈ Rq, let b: Z → R be a periodic function of period T such that b(·) = pj on sj−1 + 1, sj for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that pm ≠ pn for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1. 相似文献
11.
12.
In this paper, we present a complement of a generalized Ando-Hiai inequality due to Fujii and Kamei [M. Fujii, E. Kamei, Ando-Hiai inequality and Furuta inequality, Linear Algebra Appl. 416 (2006) 541-545]. Let A and B be positive operators on a Hilbert space H such that 0<m1?A?M1 and 0<m2?B?M2 for some scalars mi?Mi (i=1,2), and let α∈[0,1]. Put for i=1,2. Then for each 0<r?1 and s?1
13.
An even-order three-point boundary value problem on time scales 总被引:1,自引:0,他引:1
Douglas R Anderson Richard I Avery 《Journal of Mathematical Analysis and Applications》2004,291(2):514-525
We study the even-order dynamic equation (−1)nx(Δ∇)n(t)=λh(t)f(x(t)), t∈[a,c] satisfying the boundary conditions x(Δ∇)i(a)=0 and x(Δ∇)i(c)=βx(Δ∇)i(b) for 0?i?n−1. The three points a,b,c are from a time scale , where 0<β(b−a)<c−a for b∈(a,c), β>0, f is a positive function, and h is a nonnegative function that is allowed to vanish on some subintervals of [a,c] of the time scale. 相似文献
14.
Michael Bartl 《Journal of Mathematical Analysis and Applications》2007,328(1):730-742
Let n?2, Sn−1 be the unit sphere in Rn. For 0?α<1, m∈N0, 1<p?2, and Ω∈L∞(Rn)×Hr(Sn−1) with (where Hr is the Hardy space if r?1 and Hr=Lr if 1<r<∞), we study the singular integral operator, for r?1, defined by
15.
E.F. Clifford 《Journal of Mathematical Analysis and Applications》2005,312(1):195-204
We prove a value distribution result which has several interesting corollaries. Let k∈N, let α∈C and let f be a transcendental entire function with order less than 1/2. Then for every nonconstant entire function g, we have that (f○g)(k)−α has infinitely many zeros. This result also holds when k=1, for every transcendental entire function g. We also prove the following result for normal families. Let k∈N, let f be a transcendental entire function with ρ(f)<1/k, and let a0,…,ak−1,a be analytic functions in a domain Ω. Then the family of analytic functions g such that
16.
Persistence, contractivity and global stability in logistic equations with piecewise constant delays
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2002,270(2):1532-635
We establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N*=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, ∑i=0mbi>0, bi0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, 1−ax−g(x,x,…,x)=0 has a unique solution x*>0 and g(x0,x1,…,xm)C1[(0,+∞)×(0,+∞)××(0,+∞)]. 相似文献
17.
Youyu Wang Guosheng Zhang Weigao Ge 《Journal of Applied Mathematics and Computing》2006,22(1-2):361-372
In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $(\phi _p (x'(t)))' = f(t,x(t),x'(t))$ subject to the boundary value conditions: $(\phi _p (x'(0)) = \sum\limits_{i = 1}^{n - 2} {\alpha _i \phi _p (x'(\xi _i ))} $ , $(\phi _p (x'(1)) = \sum\limits_{j = 1}^{m - 2} {\beta _j \phi _p (x'(\eta _i ))} $ where ? p (s)=|s|p-2 s, p>1,αi(1≤i≤n-2)∈R,β{jit}(1≤j≤m-2)∈R, 0<ξ1<ξ2<...<ξn-2<1, 0<η1<η2<...<ηm-2<1, By applying the extension of Mawhin’s continuation theorem, we prove the existence of at least one solution. Our result is new. 相似文献
18.
Let p(z) be a polynomial of degree n having zeros |ξ1|≤???≤|ξ m |<1<|ξ m+1|≤???≤|ξ n |. This paper is concerned with the problem of efficiently computing the coefficients of the factors u(z)=∏ i=1 m (z?ξ i ) and l(z)=∏ i=m+1 n (z?ξ i ) of p(z) such that a(z)=z ?m p(z)=(z ?m u(z))l(z) is the spectral factorization of a(z). To perform this task the following two-stage approach is considered: first we approximate the central coefficients x ?n+1,. . .x n?1 of the Laurent series x(z)=∑ i=?∞ +∞ x i z i satisfying x(z)a(z)=1; then we determine the entries in the first column and in the first row of the inverse of the Toeplitz matrix T=(x i?j ) i,j=?n+1,n?1 which provide the sought coefficients of u(z) and l(z). Two different algorithms are analyzed for the reciprocation of Laurent polynomials. One algorithm makes use of Graeffe's iteration which is quadratically convergent. Differently, the second algorithm directly employs evaluation/interpolation techniques at the roots of 1 and it is linearly convergent only. Algorithmic issues and numerical experiments are discussed. 相似文献
19.
W.Y. Chan 《Journal of Computational and Applied Mathematics》2011,235(13):3831-3840
For the problem given by uτ=(ξrumuξ)ξ/ξr+f(u) for 0<ξ<a, 0<τ<Λ≤∞, u(ξ,0)=u0(ξ) for 0≤ξ≤a, and u(0,τ)=0=u(a,τ) for 0<τ<Λ, where a and m are positive constants, r is a constant less than 1, f(u) is a positive function such that limu→c−f(u)=∞ for some positive constant c, and u0(ξ) is a given function satisfying u0(0)=0=u0(a), this paper studies quenching of the solution u. 相似文献
20.
We solve the inverse spectral problem of recovering the singular potential from W−12(0,1) of a Sturm-Liouville operator by its spectra on the three intervals [0,1], [0,a], and [a,1] for some a∈(0,1). Necessary and sufficient conditions on the spectral data are derived, and uniqueness of the solution is analyzed. 相似文献