共查询到20条相似文献，搜索用时 46 毫秒
1.
Giovany M. Figueiredo Marcelo F. Furtado 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(3):309-334
We consider the quasilinear system
where , V and W are positive continuous potentials, Q is an homogeneous function with subcritical growth, with satisfying . We relate the number of solutions with the topology of the set where V and W attain it minimum values. We consider the subcritical case γ = 0 and the critical case γ = 1. In the proofs we apply Ljusternik-Schnirelmann
theory.
The second author was partially supported by FEMAT-DF 相似文献
2.
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M),
Our characterization contains a complete solution to a research problem on 2-edge-connected subgraph polyhedra posed by Cornuéjols,
Fonlupt, and Naddef in 1985, which was independently solved by Vandenbussche and Nemhauser in Vandenbussche and Nemhauser
(J. Comb. Optim. 9:357–379, 2005).
W. Zang’s research partially supported by the Research Grants Council of Hong Kong. 相似文献
3.
Elena I. Kaikina Leonardo Guardado-Zavala Hector F. Ruiz-Paredes Jesus A. Mendez Navarro 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):63-77
We study nonlinear nonlocal equations on a half-line in the critical case
where . The linear operator is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol , the number . The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem (0.1) and to find
the main term of the large time asymptotic representation of solutions in the critical case.
相似文献
4.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
where Ω is a bounded smooth domain in , and p(x) > 1 for with and φ ≢ 0 on ∂Ω. Using the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that, there exists λ* > 0 such that the problem has at least two positive solutions if λ = λ*, has at least one positive solution if λ = λ*, and has no positive solution if λ = λ*. To prove the result we establish a special strong comparison principle for the Neumann problems.
The research was supported by the National Natural Science Foundation of China 10371052,10671084). 相似文献
5.
6.
Let
be a continuous, coercive form where V is a Hilbert space, densely and continuously embedded into L2(Ω). Denote by T the associated semigroup on L2(Ω). We show that T consists of multiplication operators if and only if V is a sublattice with normal cone and
We also prove a vector-valued version of this result. For this we characterize multiplication operators
by locality. If Ω has no atoms, we show that each local, linear mapping is automatically continuous 相似文献
7.
Aleksandar Ivić 《Archiv der Mathematik》2008,90(5):412-419
If
denotes the error term in the classical Rankin-Selberg problem, then it is proved that
where Δ1(x) = ∫
x
0 Δ(u)du. The latter bound is, up to ‘ɛ’, best possible.
Received: 8 February 2007 相似文献
8.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
9.
Dimitrios Betsakos 《Mathematische Zeitschrift》2008,259(1):187-196
Let denote the density of the hyperbolic metric for a domain Ω in the extended complex plane . We prove the inequality
with C = 8.27. The inequality was proved by Sugawa and Vuorinen with C = 10.33. The proof uses monotonicity properties of the hyperbolic metric for the thrice punctured extended plane. Gardiner
and Lakic proved the inequality
with an unspecified constant C
1. We show that the best constant Σ1 in this inequality is between 3.25 and 8.27. We also prove a related conjecture formulated by Sugawa and Vuorinen.
The author was partially supported by the EPEAK programm Pythagoras II (Greece). 相似文献
10.
In this paper, we derive a local gradient estimate for the positive solution to the following parabolic equation
, where a, b are real constants, M is a complete noncompact Riemannian manifold. As a corollary, we give a local gradient estimate for the corresponding elliptic
equation:
, which improves and extends the result of Ma (J Funct Anal 241:374–382, 2006) and get a bound for the positive solution to
this elliptic equation.
相似文献
11.
Zhaoli Liu Jiabao Su Zhi-Qiang Wang 《Calculus of Variations and Partial Differential Equations》2009,35(4):463-480
In this paper, we study existence of nontrivial solutions to the elliptic equation
and to the elliptic system
where Ω is a bounded domain in with smooth boundary ∂Ω, , f (x, 0) = 0, with m ≥ 2 and . Nontrivial solutions are obtained in the case in which the nonlinearities have linear growth. That is, for some c > 0, for and , and for and , where I
m
is the m × m identity matrix. In sharp contrast to the existing results in the literature, we do not make any assumptions at infinity
on the asymptotic behaviors of the nonlinearity f and .
Z. Liu was supported by NSFC(10825106, 10831005). J. Su was supported by NSFC(10831005), NSFB(1082004), BJJW-Project(KZ200810028013)
and the Doctoral Programme Foundation of NEM of China (20070028004). 相似文献
12.
We present a norm estimate for the partial transpose map Θ on the tensor product
with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on Mm,n in terms of the spectral norm of
:
We show further that in the special case of
as well as AX + XB and AX + XBT those estimates are much improved and that
for certain Schatten p-norms.
Dedicated to the memory of late Professor Helmut H. Schaefer 相似文献
13.
We consider autonomous integrals
in the multidimensional calculus of variations, where the integrand f is a strictly W
1,p
-quasiconvex C
2-function satisfying the (p,q)-growth conditions
with exponents 1 < p ≤ q < ∞. Under these assumptions we establish an existence result for minimizers of F in provided . We prove a corresponding partial C
1,α
-regularity theorem for . This is the first regularity result for autonomous quasiconvex integrals with (p,q)-growth. 相似文献
14.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
15.
Decomposition (or concentration-compactness) lemmas have already shown their efficience in order to show existence of minimizers or ground state solutions. The aim of this paper is to apply new version of these lemmas to minimisation problems involving Hardy–Sobolev type inequalities on a specific class of unbounded domains. More precisely, we shall find ground state solution for the following quotient, where value of real numbers ,b,q and are given.
We shall end this paper by establishing a decomposition lemma for cylindrical domains. More precisely, we shall find a minimizer for the following quantity:
Transmis par le Professeur H. Brezis. 相似文献
16.
Yisheng Song 《Positivity》2009,13(4):643-655
In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by
, where f is a Lipschitz strong pseudocontractive mapping and {βn}, {αn} satisfy (i); (ii) ; (iii).
相似文献
17.
László Losonczi 《Aequationes Mathematicae》2007,74(3):262-281
Summary. Let be given continuous functions on the interval I such that g ≠ 0, and is strictly monotonic (thus invertible) on I. Taking an increasing nonconstant function μ on [0, 1]
is a mean value of . Here we solve the homogeneity equation
for two important special cases of symmetric means of this type: for the quasi-arithmetic means weighted by a weight function
and for the Cauchy means. We assume that is open, , and f, g satisfy strong differentiability conditions.
Research supported by OTKA grants T 043080, T 047373. 相似文献
18.
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
19.
In this paper we prove that any residue class λ modulo a large prime number p can be represented in the form
for some positive integers m1, n1,... ,m5, n5 of the size O(p27/28). This improves one of the results from [6] on representability of λ modulo p in the form
with
. We also prove that any residue class modulo p can be represented in the form
with
. This improves the result of [7].
Received: 27 March 2006 相似文献
20.
Given (M, g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem
has a K-peaks solution, whose peaks collapse, as ε goes to zero, to an isolated local minimum point of the scalar curvature. Here p > 2 if N = 2 and .
E. N. Dancer was partially supported by the ARC. A. M. Micheletti and A. Pistoia are supported by Mi.U.R. Project “Metodi
variazionali e topologici nello studio di fenomeni non lineari”. 相似文献