共查询到20条相似文献,搜索用时 203 毫秒
1.
《Applied Mathematics Letters》2000,13(6):7-11
Assuming f is bounded and solutions to the linearized equation are unique, the uniqueness and existence of solutions is established for solutions of the equation y(n) = f(t,y,y′,…,y(n−1)) subject to the right focal boundary conditions. 相似文献
2.
Xiaojing Yang 《Mathematische Nachrichten》2004,276(1):89-102
In this paper, we consider the unboundedness of solutions of the following differential equation (φp(x′))′ + (p ? 1)[αφp(x+) ? βφp(x?)] = f(x)x′ + g(x) + h(x) + e(t) where φp(u) = |u|p? 2 u, p > 1, x± = max {±x, 0}, α and β are positive constants satisfying with m, n ∈ N and (m, n) = 1, f and g are continuous and bounded functions such that limx→±∞g(x) ? g(±∞) exists and h has a sublinear primitive, e(t) is 2πp‐periodic and continuous. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Ming-Huat Lim 《Linear and Multilinear Algebra》2013,61(4):481-496
Let A be a non-empty set and m be a positive integer. Let ≡ be the equivalence relation defined on A m such that (x 1, …, x m ) ≡ (y 1, …, y m ) if there exists a permutation σ on {1, …, m} such that y σ(i) = x i for all i. Let A (m) denote the set of all equivalence classes determined by ≡. Two elements X and Y in A (m) are said to be adjacent if (x 1, …, x m?1, a) ∈ X and (x 1, …, x m?1, b) ∈ Y for some x 1, …, x m?1 ∈ A and some distinct elements a, b ∈ A. We study the structure of functions from A (m) to B (n) that send adjacent elements to adjacent elements when A has at least n + 2 elements and its application to linear preservers of non-zero decomposable symmetric tensors. 相似文献
4.
Yiu Tung Poon 《Linear and Multilinear Algebra》2013,61(1-3):221-223
Let A 1,…,Am be nxn hermitian matrices. Definine W(A 1,…,Am )={(xA1x ?,…xAmx ?):x?C n ,xx ?=1}. We will show that every point in the convex hull of W(A 1,…,Am ) can be represented as a convex combination of not more than k(m,n) points in W(A 1,…,Am ) where k(m,n)=min{n,[√m]+δ n 2 m+1}. 相似文献
5.
The oscillatory and asymptotic behavior of solutions of a class of nth order nonlinear differential equations, with deviating arguments, of the form (E, δ) Lnx(t) + δq(t) f(x[g1(t)],…, x[gm(t)]) = 0, where δ = ± 1 and L0x(t) = x(t), Lkx(t) = ak(t)(Lk ? 1x(t))., , is examined. A classification of solutions of (E, δ) with respect to their behavior as t → ∞ and their oscillatory character is obtained. The comparisons of (E, 1) and (E, ?1) with first and second order equations of the form y.(t) + c1(t) f(y[g1(t)],…, y[gm(t)]) = 0 and (an ? 1(t)z.(t)). ? c2(t) f(z[g1(t)],…, z[gm(t)]) = 0, respectively, are presented. The obtained results unify, extend and improve some of the results by Graef, Grammatikopoulos and Spikes, Philos and Staikos. 相似文献
6.
Fabio Zanolin 《Results in Mathematics》1992,21(1-2):224-250
We prove the existence of periodic solutions in a compact attractor of (R+)n for the Kolmogorov system x′i = xifi(t, x1, …, xn), i = l, …, n in the competitive case. Extension to differential delay equations are con- sidered too. Applications are given to Lotka-Volterra systems with periodic coefficients. 相似文献
7.
It is known that for all monotone functions f : {0, 1}n → {0, 1}, if x ∈ {0, 1}n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ? = n?α, then P[f(x) ≠ f(y)] < cn?α+1/2, for some c > 0. Previously, the best construction of monotone functions satisfying P[fn(x) ≠ fn(y)] ≥ δ, where 0 < δ < 1/2, required ? ≥ c(δ)n?α, where α = 1 ? ln 2/ln 3 = 0.36907 …, and c(δ) > 0. We improve this result by achieving for every 0 < δ < 1/2, P[fn(x) ≠ fn(y)] ≥ δ, with:
- ? = c(δ)n?α for any α < 1/2, using the recursive majority function with arity k = k(α);
- ? = c(δ)n?1/2logtn for t = log2 = .3257 …, using an explicit recursive majority function with increasing arities; and
- ? = c(δ)n?1/2, nonconstructively, following a probabilistic CNF construction due to Talagrand.
8.
In this paper, we study the existence of multiple positive solutions of boundary value problems for second-order discrete equations Δ2 x(n ? 1) ? pΔx(n ? 1) ? qx(n ? 1)+f(n, x(n)) = 0, n ∈ {1,2,…}, αx(0) ? βΔx(0) = 0, x(∞) = 0. The proofs are based on the fixed point theorem in Fréchet space (see Agarwal and O'Regan, 2001, Cone compression and expansion and fixed point theorems in Fréchet spaces with application, Journal of Differential Equations, 171, 412–42). 相似文献
9.
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F n (f)}, where F n (x) = F(x) * δ n (x) and {δ n (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x ?s ln m |x| and x r is proved to exist and be equal to r m x ?rs ln m |x| for r, s, m = 2, 3…. 相似文献
10.
R. Abu-Saris K. Al-Dosary Q. Al-Hassan 《Journal of Difference Equations and Applications》2013,19(10):869-877
We consider difference equations of order k n+k ≥ 2 of the form: yn+k = f(yn,…,yn+k-1), n= 0,1,2,… where f: D k → D is a continuous function, and D?R. We develop a necessary and sufficient condition for the existence of a symmetric invariant I(x 1,…,xk ) ∈C∞[Dk,D]. This condition will be used to construct invariants for linear and rational difference equations. Also, we investigate the transformation of invariants under invertible maps. We generalize and extend several results that have been obtained recently. 相似文献
11.
S. -M. Jung 《Acta Mathematica Hungarica》2009,124(1-2):155-163
We solve the inhomogeneous linear first order differential equations of the form y′(x) ? λy(x) = Σ m=0 ∞ a m (x ? c) m , and prove an approximation property of exponential functions. More precisely, we prove the local Hyers-Ulam stability of linear first order differential equations of the form y′(x) = λy(x) in a special class of analytic functions. 相似文献
12.
Thomas H. Pate 《Linear and Multilinear Algebra》2013,61(1-4):253-259
Lek k be an infinite field and suppose m.i. and n are positive integers such that t m We study the subset of k[x 1,x 2, … xm ] which consists of 0 and the homogeneous members t of f of k[x 1,x 2, … xm ] of fixed degree n such that there exists homogeneous F 1, F 2, … Ft in k[x 1,x 2, … xm ] of degree one and homogenous g 1 g 2, …gt , in k[x 1,x 2, … xm ] such that f(x) = F 1(x)g 1(x) + F 2(x)g 2(x) + … + F t (x)g t (x) for each x in k m. In case k is algebrarcally closed we are able to prove that this set is an algebraic variety. Consequently. if k is also of characteristic 0 then we are able to prove that certain collections of symmetric k-valued multilinear functions are algebraic varieties. 相似文献
13.
P. K. SAHO 《数学学报(英文版)》2005,21(5):1159-1166
In this paper, we determine the general solution of the functional equation f1 (2x + y) + f2(2x - y) = f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 : R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) = g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. 相似文献
14.
A comparative study of the functional equationsf(x+y)f(x–y)=f
2(x)–f
2(y),f(y){f(x+y)+f(x–y)}=f(x)f(2y) andf(x+y)+f(x–y)=2f(x){1–2f
2(y/2)} which characterise the sine function has been carried out. The zeros of the functionf satisfying any one of the above equations play a vital role in the investigations. The relation of the equationf(x+y)+f(x–y)=2f(x){1–2f
2(y/2)} with D'Alembert's equation,f(x+y)+f(x–y)=2f(x)f(y) and the sine-cosine equationg(x–y)=g(x)g(y) +f(x)f(y) has also been investigated. 相似文献
15.
R. Wolf 《Archiv der Mathematik》2001,76(4):308-313
Abstract. We prove the following result: Let X be a compact connected Hausdorff space and f be a continuous function on X x X. There exists some regular Borel probability measure m\mu on X such that the value of¶¶ ò\limit X f(x,y)dm(y)\int\limit _X f(x,y)d\mu (y) is independent of the choice of x in X if and only if the following assertion holds: For each positive integer n and for all (not necessarily distinct) x1,x2,...,xn,y1,y2,...,yn in X, there exists an x in X such that¶¶ ?i=1n f(xi,x)=?i=1n f(yi,x).\sum\limits _{i=1}^n f(x_i,x)=\sum\limits _{i=1}^n f(y_i,x). 相似文献
16.
Pierre Maréchal 《Mathematical Programming》2001,89(3):505-516
It is well known that a function f of the real variable x is convex if and only if (x,y)→yf(y
-1
x),y>0 is convex. This is used to derive a recursive proof of the convexity of the multiplicative potential function. In this
paper, we obtain a conjugacy formula which gives rise, as a corollary, to a new rule for generating new convex functions from
old ones. In particular, it allows to extend the aforementioned property to functions of the form (x,y)→g(y)f(g(y)-1
x) and provides a new tool for the study of the multiplicative potential and penalty functions.
Received: June 3, 1999 / Accepted: September 29, 2000?Published online January 17, 2001 相似文献
17.
In the previous researches [2,3] b-integer and b-decimal parts of real numbers were introduced and studied by M.H. Hooshmand. The b-parts real functions have many interesting number theoretic explanations, analytic and algebraic properties, and satisfy the functional equation f (f(x) + y - f(y)) = f(x). These functions have led him to a more general topic in semigroups and groups (even in an arbitrary set with a binary operation [4] and the following functional equations have been introduced: Associative equations:
f(xf(yz))=f(f(xy)z),f(xf(yz))=f(f(xy)z)=f(xyz)