共查询到20条相似文献,搜索用时 31 毫秒
1.
P.S Milojević 《Journal of Mathematical Analysis and Applications》1978,65(2):468-502
Let X and Y be real normed spaces with an admissible scheme Γ = {En, Vn; Fn, Wn} and T: X → 2YA-proper with respect to Γ such that dist(y, A(x)) < kc(∥ x ∥) for all y in T(x) with ∥ x ∥ ? R for some R > 0 and k > 0, where c: R+ → R+ is a given function and A: X → 2Y a suitable possibly not A-proper mapping. Under the assumption that either T or A is odd or that (u, Kx) ? 0 for all u in T(x) with , we obtain (in a constructive way) various generalizations of the first Fredholm theorem. The unique approximation-solvability results for the equation T(x) = f with T such that T(x) ? T(y) ?A(x ? y) for x, y in X or T is Fréchet differentiable are also established. The abstract results for A-proper mappings are then applied to the (constructive) solvability of some boundary value problems for quasilinear elliptic equations. Some of our results include the results of Lasota, Lasota-Opial, Hess, Ne?as, Petryshyn, and Babu?ka. 相似文献
2.
Steven D Taliaferro 《Journal of Differential Equations》1984,54(1):19-59
Under the condition that f(x, y, z, α) and its partial derivatives decay sufficiently fast as we will study the (linear) stability and bifurcation of equilibrium solutions of the scalar problem ut = uxx + f(x, u, ux, α), ux(?∞, t) = ux(∞, t) = 0 (1) where α is a real bifurcation parameter. After introducing appropriate function spaces X and Y the problem (1) can be rewritten , (7) where G:X×R → Y is given by G(u, α)(x) = u″(x) + f(x, u(x), u′(x), α). It will be shown, for each (u, α)?X × R, that the Fréchet derivative Gu(u,a): X → Y is not a Fredholm operator. This difficulty is due to the fact that the domain of the space variable x, is infinite and cannot be eliminated by making another choice of X and Y. Since Gu(u, α) is not Fredholm, the hypotheses of most of the general stability and bifurcation results are not satisfied. If (u0, α0?S = {(u, α): G(u, α) = 0}, (i.e., (u0,α0) is an equilibrium solution of (7)), a necessary condition on the spectrum of Gu(u0, α0) for a change in the stability of points in S to occur at Gu(u0, α0) will be given. When this condition is met, the principle of exchange of stability which means, in a neighborhood of (u0, α0), that adjacent equilibrium solutions for the same α have opposite stability properties in a weakened sense will be established. Also, when Gu or its first order partial derivatives, evaluated at (u0, α0), are not too degenerate, the shape of S in a neighborhood of (u0, α0) will be described and a strenghtened form of the principle of exchange of stability will be obtained. 相似文献
3.
《Journal de Mathématiques Pures et Appliquées》2002,81(9):827-846
We consider the system Δu=p(x)g(v), Δv=q(x)f(u) in , where f,g are positive and non-decreasing functions on (0,∞) satisfying the Keller–Osserman condition and we establish the existence of positive solutions that blow-up at infinity. 相似文献
4.
Tomás Domínguez Benavides 《Journal of Mathematical Analysis and Applications》1985,105(1):176-186
Let X be a Banach space, C a bounded closed subset of X, A a convex closed subset of X, a complete metric space formed by all α-nonexpansive mappings fC → A and a complete metric space formed by α-nonexpansive differentiable mappings fC → X. The following assertions are proved in this paper: (1) Properness of I ? f is a generic property in (2)the subset of formed by all α-contractive mappings is of Baire first category in ; and (3) for every y?X, the functional equation x ? f(x) = y has generically a finite number of solutions for f in . Some applications to the fixed point theory and calculation of the topological degree are given. 相似文献
5.
Claudio Morales 《Journal of Mathematical Analysis and Applications》1985,105(1):167-175
Let X be a Banach space with the dual space to be uniformly convex, let D ? X be open, and let be strongly accretive (i.e., for some k < 1: (λ ? k)∥ u ? v∥ ? ∥(λ ? 1)(u ? v)+ T(u) ? T(v)∥ for all and λ > k). Suppose T is demicontinuous and strongly accretive and suppose there exists z?D satisfying: T(x) t(x ? z) for all x??D and t < 0. Then it is shown that T has a unique zero in . This result is then applied to the study of existence of zeros of accretive mappings under apparently different types of boundary conditions on T. 相似文献
6.
《Nonlinear Analysis: Theory, Methods & Applications》2004,57(2):173-181
Let be a measurable space, X and Y separable Banach spaces, and C a weakly compact subset of X. Let and be continuous random operators. Then the deterministic solvability of the equationimplies the stochastic solvability of it provided that (f−T)(ω,.) is demiclosed at zero and T(ω,C) is bounded for each . As applications, random fixed points of various types of pseudo-contractive and k-set-contractive random operators are obtained. 相似文献
7.
J Globevnik 《Journal of Functional Analysis》1976,22(1):32-38
Denote by Δ(resp. ) the open (resp. closed) unit disc in C. Let E be a closed subset of the unit circle T and let F be a relatively closed subset of T ? E of Lesbesgue measure zero. The following result is proved. Given a complex Banach space X and a bounded continuous function f:F → X, there exists an extension f? of f, bounded and continuous on , analytic on Δ and satisfying sup. This is applied to show that for any separable complex Banach space X there exists an analytic function from Δ to X whose range is contained and dense in the unit ball of X. 相似文献
8.
Anna Maria Mantero 《Journal of Functional Analysis》1982,47(1):7-25
Let K be a distribution on 2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∝∝ dudvK(x ? u, y ? v) f(u, v) exp(ixv ? iyu). We show that there exists K such that the operator λ(K) is bounded on Lp(R)2 for every p in (1, 2¦, but is unbounded on Lq(R)2 for every q > 2. 相似文献
9.
We investigate the boundary value problem , , u(?∞, t) = v(∞, t) = 0, u(∞, t) = 1, and v(?∞, t) = γ ?t > 0 where r > 0, b > 0, γ > 0 and x?R. This system has been proposed by Murray as a model for the propagation of wave fronts of chemical activity in the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We determine the global stability of the constant solution (u, v) ≡ (1,0). Furthermore we introduce a moving coordinate and for each fixed x?R we investigate the asymptotic behavior of u(x + ct, t) and v(x + ct, t) as t → ∞ for both large and small values of the wave speed c ? 0. 相似文献
10.
Igor Kluvánek 《Journal of Functional Analysis》1976,21(3):316-329
For a set K in a locally convex topological vector space X there exists a set T, a σ-algebra of subsets of T and a σ-additive measure m: → X such that K is the closed convex hull of the range {m(E): E ∈ } of the measure m if and only if there exists a conical measure u on X so that K Ku,Ku, the set of resultants of all conical measures v on X such that v < u. 相似文献
11.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
12.
The existence of periodic solutions near resonance is discussed using elementary methods for the evolution equation ·u = Au + ?f(t, u) when the linear problem is totally degenerate (e2πA = I) and the period of f is entrained with ? (T = 2π(1 + ?μ)). The approach is to solve the periodicity equation u(T,p,?) = p for an element p(?) in D, the domain of A, as a perturbation from an approximate solution p0. p0 is a solution of the nonlinear boundary value problem 2πμAp + ∝02πe?Asf(s, eAsp) ds = 0 obtained from the periodicity equation by dividing by ?, applying the entrainment assumption, and letting ? → 0. Once p0 is known, the conventional inverse function theorem is applied in a slightly unconventional manner. Two particular cases where results are obtained are ut = ux + ?{g(u) ? h(t, x)} with g strongly monotone and , where in both cases D is a certain class of 2π-periodic functions of x. 相似文献
13.
Hsin Chu 《Journal of Mathematical Analysis and Applications》1982,85(2):566-583
Let X and Y be Banach spaces, ; P is said to be strongly ?-accretive if for some c > 0 and each x,y?X. These mappings constitute a generalization simultaneously of monotone mappings () and accretive mappings (when Y = X). By applying a theorem of 1. Ekeland, it is shown that a localized class of these mappings must be surjective under appropriate geometric assumptions on and continuity assumptions on P. The results generalize two theorems of F. E. Browder and the proofs further refine the methodology for dealing with such mappings. 相似文献
14.
The following result, and a closely related one, is proved: If u:X → Y is an open, perfect surjection, with X metrizable and with dim X = 0 or dim Y = 0, then there exists a perfect surjection such that u ° h = πY (where S in the Cantor set and is the projection). If moreover, u-1(y) is homeomorphic to S for all y?Y, then h can be chosen to be a homeomorphism. 相似文献
15.
Samuel M Rankin 《Journal of Mathematical Analysis and Applications》1982,88(2):531-542
Existence and asymptotic behavior of solutions are given for the equation u′(t) = ?A(t)u(t) + F(t,ut) (t ? 0) and u0 = ? ? C([?r,0]; X) C. The space X is a Banach space; the family of unbounded linear operators defined on D(A) ? X → X generates a linear evolution system and F: C → X is continuous with respect to a fractional power of A(t0) for some t0 ? [0, T]. 相似文献
16.
Let be a smooth bounded domain in . Assume that f?0 is a C1-function on [0,∞) such that f(u)/u is increasing on (0,+∞). Let a be a real number and let b?0, b?0 be a continuous function such that b≡0 on . The purpose of this Note is to establish the asymptotic behaviour of the unique positive solution of the logistic problem Δu+au=b(x)f(u) in , subject to the singular boundary condition u(x)→+∞ as . Our analysis is based on the Karamata regular variation theory. To cite this article: F.-C. Cîrstea, V. R?dulescu, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
17.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
18.
David W Bange Anthony E Barkauskas Peter J Slater 《Journal of Combinatorial Theory, Series B》1985,38(1):31-40
If G is a connected graph having no vertices of degree 2 and L(G) is its line graph, two results are proven: if there exist distinct edges e and f with L(G) ? e ? L(G) ? f then there is an automorphism of L(G) mapping e to f; if for any distinct vertices u, v, then for any distinct edges e, f. 相似文献
19.
Wolfgang Ruess 《Journal of Mathematical Analysis and Applications》1981,84(2):400-417
This is a study of compactness in (a) spaces Kb(X, Y) of compact linear operators, (b) injective tensor products , and (c) spaces Lc(X, Y) of continuous linear operators, and its various relationships with equicontinuity and collective compactness. Among the applications is a result on factoring compact sets of compact operators compactly and uniformly through one and the same reflexive Banach space. 相似文献
20.
Christopher K.R.T. Jones 《Journal of Differential Equations》1983,49(1):142-169
Two theorems are proved for the spherically symmetric solutions of the “bistable” reaction-diffusion equation , where ? is cubic-like and x ∈ Rn. The first theorem says that, for a suitable class of initial data, there are only two types of asymptotic behavior, u(x, t) tends to an equilibrium solution as t → + ∞ or u(x, t) → 1 uniformly on compact sets. The second theorem says that in the latter case, if the solution is followed out along any ray, it approaches, in shape, the one-dimensional travelling wave. 相似文献