共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper deals with the solvability of the boundary value problem
where p ∈ (1, ∞) is fixed, is convex, proper, lower semicontinuous, is a Carathéodory mapping and .
Received: 12 February 2007 相似文献
2.
In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line
where is the increasing homeomorphism and positive homomorphism and . We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term
by using the five functionals fixed-point theorem.
Project supported by Foundation of Major Project of Science and Technology of Chinese Education Ministry, SRFDP of Higher
Education, NSF of Education Committee of Jiangsu Province and Project of Graduate Education Innovation of Jiangsu Province. 相似文献
3.
Gioconda Moscariello Carlo Sbordone 《Journal of Fixed Point Theory and Applications》2007,1(2):337-350
Let
be a sequence of Borel measurable functions satisfying, for a function
the inequalities
and suppose
Then there exists a sequence of increasing homeomorphisms
converging to a homeomorphism
weakly in
and locally uniformly, such that
Dedicated to the memory of Jean Leray 相似文献
4.
The existence of multiple positive solutions is presented for the singular second-order boundary value problems
using the fixed point index, where f may be singular at x = 0 and x′ = 0.
The project is supported by the fund of natural science of Shandong Province. 相似文献
5.
On a periodic boundary value problem for cyclic feedback type linear functional differential systems
Sulkhan Mukhigulashvili 《Archiv der Mathematik》2006,87(3):255-260
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
where ω > 0, ℓi : C([0, ω])→ L([0,ω]) are linear bounded operators, and qi∈L([0, ω]).
Received: 11 June 2005 相似文献
6.
WUSHAOPING YANGHAITAO 《高校应用数学学报(英文版)》1998,13(3):251-262
Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x f(t,x)=0 are given by means of variational methods, where the function -1/2a(t)|s|^2∫^t0f(t,s)ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t 1 t a(t)dt= ∞,VI∈R^1.A resonance case as well as a noncompact case is discussed too. 相似文献
7.
A detailed analysis is made of the structure of positive solutions of fourth-order differential equations of the form
under the assumption that α, β are positive constants, p(t), q(t) are positive continuous functions on [a,∞), and p(t) satisfies
Mathematics Subject Classification (2000) 34C10, 34D05 相似文献
8.
By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order
two-point boundary value problem
is obtained under some conditions of growth, where α, β, γ, δ ≥ 0, ρ = αγ + γβ + δα > 0, and h(t) is allowed to be singular at t = 0 and t = 1.
Supported by the National Natural Science Foundation of China(10771031,10671167). 相似文献
9.
We consider the Allen–Cahn equation
where Ω is a smooth and bounded domain in
such that the mean curvature is positive at each boundary point. We show that there exists a sequence ε j → 0 such that the Allen–Cahn equation has a solution
with an interface which approaches the boundary as j → + ∞. 相似文献
10.
Huaning Liu 《Bulletin of the Brazilian Mathematical Society》2007,38(2):179-188
For integers a,
b and n
> 0, define
and
where
denotes the summation over all
r such that (r, n) = 1, and
is defined by the equation
. The two sums are analogous to the
homogeneous Dedekind sum S(a,b,
n). The functional equations for
A
Γ and B
Γ are established. Furthermore, Knopp's
identity on Dedekind sum is extended.
*This work is supported by the N.S.F. (10271093,
60472068) of P.R. China. 相似文献
11.
Xia Chen 《Journal of Theoretical Probability》1999,12(2):421-445
Let {X
n
}
n0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure , and let f be a real measurable function on E. We prove that with probability one,
under some best possible conditions. 相似文献
12.
Let
and
. We are interested in the lower bounds of the integral:
where h > 0 and
. Using the lower bounds for these integrals we obtain in particular for the so-called Fejér operator
of
the following asymptotic expression
which essentially improves the results concerning the approximation behavior of this operator.
Received: 10 January 2006 相似文献
13.
14.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
15.
Antonio Cañada Juan A. Montero Salvador Villegas 《Mediterranean Journal of Mathematics》2006,3(2):177-187
Let us consider the linear boundary value problem
where
and
is defined by
Classical Lyapunov inequality states that
for any function
where
The constant 4/L is optimal. Let us note that Lyapunov inequality is given in terms of
the usual norm in the space L1(0, L). In this paper we review some recent results on Lp Lyapunovtype inequalities,
, for ordinary and partial differential equations on a bounded and regular domain in
In the last case, it is showed that the relation between the quantities p and N/2 plays a crucial role, pointing out a deep difference with respect to the ordinary case. In the proof, the best constants
are obtained by using a related variational problem and Lagrange multiplier theorem. Finally, the linear results are combined
with Schauder fixed point theorem in the study of resonant nonlinear problems.
The authors have been supported by the Ministry of Science and Technology of Spain MTM2005- 01331 and by Junta de Andalucia
(FQM116). 相似文献
((0.1)) |
16.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
17.
18.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
19.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
20.
Sun Zhonghua Qi Wenfeng 《高校应用数学学报(英文版)》2007,22(4):469-477
Let Z/(pe) be the integer residue ring modulo pe with p an odd prime and integer e ≥ 3. For a sequence (a) over Z/(pe), there is a unique p-adic decomposition (a) = (a)0 (a)1·p … (a)e-1 ·pe-1, where each (a)i can be regarded as a sequence over Z/(p), 0 ≤ i ≤ e - 1. Let f(x) be a primitive polynomial over Z/(pe) and G' (f(x), pe) the set of all primitive sequences generated by f(x) over Z/(pe). For μ(x) ∈ Z/(p)[x] with deg(μ(x)) ≥ 2 and gcd(1 deg(μ(x)),p- 1) = 1,set ψe-1 (x0, x1,…, xe-1) = xe-1·[ μ(xe-2) ηe-3 (x0, x1,…, xe-3)] ηe-2 (x0, x1,…, xe-2),which is a function of e variables over Z/(p). Then the compressing map ψe-1: G'(f(x),pe) → (Z/(p))∞,(a) (→)ψe-1((a)0, (a)1,… ,(a)e-1) is injective. That is, for (a), (b) ∈ G' (f(x), pe), (a) = (b) if and only if ψe - 1 ((a)0, (a)1,… , (a)e - 1) =ψe - 1 ((b)0,(b)1,… ,(b)e-1). As for the case of e = 2, similar result is also given. Furthermore, if functions ψe-1 and ψe-1 over Z/(p) are both of the above form and satisfy ψe-1((a)0,(a)1,… ,(a)e-1) = ψe-1((b)0,(b)1,… ,(b)e-1) for (a),(b) ∈ G'(f(x),pe), the relations between (a) and (b), ψe-1 and ψe-1 are discussed. 相似文献