Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

The following system considered in this paper:

Best constant in a three-parameter Poincaré inequality

We study the problem of finding the best constant in the generalized Poincaré inequality

Solvability of boundary-value problems for nonlinear fractional differential equations

We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations

On the problem of determining the parameter of a parabolic equation

We study the boundary-value problem of determining the parameter p of a parabolic equation

Existence and uniqueness of positive solutions to nonlinear fractional differential equation with integral boundary conditions

In this paper, we consider the following nonlinear fractional three-point boundary-value problem:

Quenching phenomena for a non-local diffusion equation with a singular absorption

In this paper we study the quenching problem for the non-local diffusion equation

Quantitative form of the Luzin <Emphasis Type="Italic">C</Emphasis>-property

We prove the following statement, which is a quantitative form of the Luzin theorem on C-property: Let (X, d, μ) be a bounded metric space with metric d and regular Borel measure μ that are related to one another by the doubling condition. Then, for any function f measurable on X, there exist a positive increasing function η ∈ Ω (η(+0) = 0 and η(t)t ^−a decreases for a certain a > 0), a nonnegative function g measurable on X, and a set E ⊂ X, μE = 0 , for which

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: $({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.$ Here, ${(A(t))_{t\in [0,T]}}In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E:

(SE)    {ll dU(t) = (A(t)U(t) +F(t,U(t))) dt + B(t,U(t)) dWH(t),     t ? [0,T], U(0) = u0.({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.      9. On global transformations of ordinary differential equations of the second order      Václav Tryhuk 《Czechoslovak Mathematical Journal》2000,50(3):499-508 The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form f( t,uy,wy + uuz ) = f( x,y,z )u2 u+ g( t,x,u,u,w )uz + h( t,x,u,u,w )y + 2uwzf\left( {t,\upsilon y,wy + u\upsilon z} \right) = f\left( {x,y,z} \right)u^2 \upsilon + g\left( {t,x,u,\upsilon ,w} \right)\upsilon z + h\left( {t,x,u,\upsilon ,w} \right)y + 2uwz      10. An inverse spectral theorem for Kre?n strings with a negative eigenvalue      Harald Woracek 《Monatshefte für Mathematik》2012,33(3):105-149 A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ￥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L2(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D\mathfrakmDx{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as f￠(x) + z ò0L f(y) d\mathfrakm(y) = 0,    x ? \mathbb R, f￠(0-) = 0.f^{\prime}(x) + z \int_0^L f(y)\,d\mathfrak{m}(y) = 0,\quad x \in\mathbb R,\ f^{\prime}(0-) = 0.      11. 具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性   总被引：6，自引：0，他引：6   李必文  曾宪武 《高校应用数学学报(英文版)》2003,18(1):1-8 § 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…      12. Criteria of exponential decay for eigenfunctions of some classes of integral operators      V. M. Kaplitsky 《Journal of Mathematical Sciences》2010,165(4):455-462 We study sufficient conditions for exponential decay at infinity for eigenfunctions of a class of integral equations in unbounded domains in ℝ n . We consider integral operators K whose kernels have the form k( x,y ) = c( x,y )\frace - a| x - y || x - y |b , ( x,y ) ? W×W, k\left( {x,y} \right) = c\left( {x,y} \right)\frac{{{e^{ - \alpha \left| {x - y} \right|}}}}{{{{\left| {x - y} \right|}^\beta }}},\,\left( {x,y} \right) \in \Omega \times \Omega,      13. A bound for the error of the Ritz method in the case of the Lidstone problem for a singular differential equation of fourth order      M. N. Yakovlev 《Journal of Mathematical Sciences》2010,165(5):601-605 For the Lidstone boundary-value problem *20c u(4) + q(t)u = f(t),   0 < t < 1, u(0) = u"(0) = u(1) = u"(1) = 0 \begin{array}{*{20}{c}} {{u^{(4)}} + q(t)u = f(t),\,\,\,0 < t < 1,} \\ {u(0) = u'(0) = u(1) = u'(1) = 0} \\ \end{array}      14. Approximation of several dimensional functions by trigonometric polynomials      Minde Cheng  Yonghe Chen 《Frontiers of Mathematics in China》2006,1(4):499-516 Let f(x, y) be a periodic function defined on the region D with period 2π for each variable. If f(x, y) ∈ C p (D), i.e., f(x, y) has continuous partial derivatives of order p on D, then we denote by ω α,β(ρ) the modulus of continuity of the function and write For p = 0, we write simply C(D) and ω(ρ) instead of C 0(D) and ω 0(ρ). Let T(x,y) be a trigonometrical polynomial written in the complex form We consider R = max(m 2 + n 2)1/2 as the degree of T(x, y), and write T R(x, y) for the trigonometrical polynomial of degree ⩾ R. Our main purpose is to find the trigonometrical polynomial T R(x, y) for a given f(x, y) of a certain class of functions such that attains the same order of accuracy as the best approximation of f(x, y). Let the Fourier series of f(x, y) ∈ C(D) be and let Our results are as follows Theorem 1 Let f(x, y) ∈ C p(D (p = 0, 1) and Then holds uniformly on D. If we consider the circular mean of the Riesz sum S R δ (x, y) ≡ S R δ (x, y; f): then we have the following Theorem 2 If f(x, y) ∈ C p (D) and ω p(ρ) = O(ρ α (0 < α ⩾ 1; p = 0, 1), then holds uniformly on D, where λ 0 is a positive root of the Bessel function J 0(x) It should be noted that either or implies that f(x, y) ≡ const. Now we consider the following trigonometrical polynomial Then we have Theorem 3 If f(x, y) ∈ C p(D), then uniformly on D, Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundarm, and Theorem 3 is a generalization of a theorem of Zygmund, which can be extended to the multiple case as follows Theorem 3′ Let f(x 1, ..., x n) ≡ f(P) ∈ C p and let where and being the Fourier coefficients of f(P). Then holds uniformly. __________ Translated from Acta Scientiarum Naturalium Universitatis Pekinensis, 1956, (4): 411–428 by PENG Lizhong.      15. Multiplicative type functional equations arising from characterization problems      Károly Lajkó  Fruzsina Mészáros 《Aequationes Mathematicae》2012,83(3):199-208 We give the general and the so-called density function solutions of equation lllfU(x)fV(y)=fX(\frac1-y1-xy ) fY (1-xy) \fracy1-xy        ( (x, y) ? (0,1)2 )\begin{array}{lll}f_{U}(x)f_{V}(y)=f_{X}\left(\frac{1-y}{1-xy} \right) f_{Y} (1-xy) \frac{y}{1-xy} \qquad \left( (x, y) \in (0,1)^2 \right)\end{array}      16. Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations      V.Yu. Slyusarchuk 《Ukrainian Mathematical Journal》2010,62(6):970-981 Let E be a finite-dimensional Banach space, let C0(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C 0(R ,E) → C 0(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C 0(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation \fracdx(t)dt + ( Kx )(t)Ax(t) = h(t),    t ? \mathbbR \frac{{dx(t)}}{{dt}} + \left( {Kx} \right)(t)Ax(t) = h(t),\quad t \in \mathbb{R}      17. On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type      Jong Yeoul Park  Jeong Ja Bae 《Czechoslovak Mathematical Journal》2002,52(4):781-795 Let be a bounded domain in #x211D;n with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem: where M is a C 1-function such that M() 0 > 0 for every 0 and f(y) = |y| y for 0.      18. Numerical verification of condition for approximately midconvex functions      P. Spurek  Ja. Tabor 《Aequationes Mathematicae》2012,83(3):223-237 Let X be a normed space and V be a convex subset of X. Let a\colon \mathbbR+ ? \mathbbR+{\alpha \colon \mathbb{R}_+ \to \mathbb{R}_+}. A function f \colon V ? \mathbbR{f \colon V \to \mathbb{R}} is called α-midconvex if f (\fracx + y2)-\fracf(x) + f(y)2 ￡ a(||x - y||)    for  x, y ? V.f \left(\frac{x + y}{2}\right)-\frac{f(x) + f(y)}{2}\leq \alpha(\|x - y\|)\quad {\rm for} \, x, y \in V.      19. Functional inequalities related to Mahler’s conjecture      M. Fradelizi  M. Meyer 《Monatshefte für Mathematik》2010,256(2):13-25 Extending a result of Meyer and Reisner (Monatsh Math 125:219–227, 1998), we prove that if g: \mathbbR? \mathbbR+{g: \mathbb{R}\to \mathbb{R}_+} is a function which is concave on its support, then for every m > 0 and every z ? \mathbbR{z\in\mathbb{R}} such that g(z) > 0, one has ò\mathbbR g(x)mdxò\mathbbR (g*z(y))m dy 3 \frac(m+2)m+2(m+1)m+3, \int\limits_{\mathbb{R}} g(x)^mdx\int\limits_{\mathbb{R}} (g^{*z}(y))^m dy\ge \frac{(m+2)^{m+2}}{(m+1)^{m+3}},      20. Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions      V. F. Babenko  N.V. Parfinovych  S. A. Pichugov 《Ukrainian Mathematical Journal》2010,62(3):343-357 Let C( \mathbbRm ) C\left( {{\mathbb{R}^m}} \right) be the space of bounded and continuous functions x:\mathbbRm ? \mathbbR x:{\mathbb{R}^m} \to \mathbb{R} equipped with the norm || x ||C = || x ||C( \mathbbRm ): = sup{ | x(t) |:t ? \mathbbRm } \left\| x \right\|C = {\left\| x \right\|_{C\left( {{\mathbb{R}^m}} \right)}}: = \sup \left\{ {\left| {x(t)} \right|:t \in {\mathbb{R}^m}} \right\}      设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号

On global transformations of ordinary differential equations of the second order

The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form

An inverse spectral theorem for Kre?n strings with a negative eigenvalue

A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ￥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L²(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D_\mathfrakmD_x{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as

具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…     

Criteria of exponential decay for eigenfunctions of some classes of integral operators

We study sufficient conditions for exponential decay at infinity for eigenfunctions of a class of integral equations in unbounded domains in ℝ ⁿ . We consider integral operators K whose kernels have the form

A bound for the error of the Ritz method in the case of the Lidstone problem for a singular differential equation of fourth order

For the Lidstone boundary-value problem

Approximation of several dimensional functions by trigonometric polynomials

Let f(x, y) be a periodic function defined on the region D

Multiplicative type functional equations arising from characterization problems

We give the general and the so-called density function solutions of equation

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Let E be a finite-dimensional Banach space, let C⁰(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C ⁰(R ,E) → C ⁰(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C ⁰(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation

On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

Let be a bounded domain in #x211D;ⁿ with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem:

Numerical verification of condition for approximately midconvex functions

Let X be a normed space and V be a convex subset of X. Let a\colon \mathbbR₊ ? \mathbbR₊{\alpha \colon \mathbb{R}_+ \to \mathbb{R}_+}. A function f \colon V ? \mathbbR{f \colon V \to \mathbb{R}} is called α-midconvex if

Functional inequalities related to Mahler’s conjecture

Extending a result of Meyer and Reisner (Monatsh Math 125:219–227, 1998), we prove that if g: \mathbbR? \mathbbR₊{g: \mathbb{R}\to \mathbb{R}_+} is a function which is concave on its support, then for every m > 0 and every z ? \mathbbR{z\in\mathbb{R}} such that g(z) > 0, one has

Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions

Let C( \mathbbR^m ) C\left( {{\mathbb{R}^m}} \right) be the space of bounded and continuous functions x:\mathbbR^m ? \mathbbR x:{\mathbb{R}^m} \to \mathbb{R} equipped with the norm