共查询到20条相似文献,搜索用时 15 毫秒
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We develop the Krasnoselskii–Krein type of uniqueness theorem for an initial value problem of the Riemann–Liouville type fractional differential equation which involves a function of the form f?(t,?x(t),?D q?1 x(t)), for 1<q<2 and establish the convergence of successive approximations. We prove a few other uniqueness theorems. 相似文献
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Summary We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations.
These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations
and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous.
We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential
equation of the general form (|x'|α-1x')' + a(t) |x|α-1x = 0. 相似文献
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In this work, we study a general class of partial neutral functional differential equations. We assume that the linear part
generates an analytic semigroup and the nonlinear part is Lipschitz continuous with respect to the é-norm associated to the
linear part. We discuss the existence, uniqueness, regularity and stability of solutions. Our results are illustrated by an
example. This work extends previous results on partial functional differential equations (Fitzgibbon and Parrot, Nonlinear
Anal., TMA 16, 479–487 (1991), Hale, Rev. Roum. Math. Pures Appl. 39, 339–344 (1994), Hale, Resen. Inst. Mat. Estat. Univ. Sao Paulo 1, 441–457 (1994), Travis and Webb, Trans. Am. Math. Soc. 240 129–143 (1978), Wu and Xia, J. Differ. Equ. 124 247–278 (1996)).
Mathematics Subject Classification (1991) 34K20, 34K30, 34K40, 47D06 相似文献
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The nonlinear Levin's comparison theorems for nonlinear second order differential equations have been established by using a modified Levin's technique. 相似文献
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Sui Sun Cheng 《Journal of Difference Equations and Applications》2013,19(4):375-387
Sturmian comparison theorems are derived for a class of discrete hyperbolic type equations. 相似文献
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In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants. 相似文献
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Introducing the notion of the formal continued fractions solutions of the generalized second order Riccati equations, one
can compute either a rational approximation of the solution or a rational solution and perform a location of the singularities
in the complex plane.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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M. B. Suryanarayana 《Journal of Optimization Theory and Applications》1976,19(1):47-61
Integral representations are obtained for solutions of a Darboux problem in a rectangle and used to prove Neustadt-type existence theorems for optimal control problems with trajectories satisfying linear, hyperbolic partial differential equations with Darboux-type boundary data. The proof bears on the fact that, in this situation, for each generalized solution, there is a usual solution where the functional takes the same value.This work was done in the framework of Research Project AFOSR-69-1662. The author is greatly indebted to Professor L. Cesari for his valuable guidance and constant encouragement during the writing of this paper. 相似文献
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Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator 下载免费PDF全文
Hasib Khan Cemil Tun Wen Chen Aziz Khan 《Journal of Applied Analysis & Computation》2018,8(4):1211-1226
In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results. 相似文献
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By means of a monotone iterative technique, we establish the existence and uniqueness of the positive solutions for a class of higher conjugate-type fractional differential equation with one nonlocal term. In addition, the iterative sequences of solution and error estimation are also given. In particular, this model comes from economics, financial mathematics and other applied sciences, since the initial value of the iterative sequence can begin from an known function, this is simpler and helpful for computation. 相似文献
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We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered. 相似文献
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Ronald Begg 《Journal of Mathematical Analysis and Applications》2006,322(2):1168-1187
A class of nonlocal second-order ordinary differential equations of the form
y″(x)=f(x,y(x),(y○λ)(x),y′(x)) 相似文献
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JiangJianchu LiXiaoping 《高校应用数学学报(英文版)》2001,16(3):244-250
Abstract. New oscillation criteria for the second order perturbed differential equation are pre-sented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results. 相似文献
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This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function. 相似文献
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Fourier expansion based recursive algorithms for periodic Riccati and Lyapunov matrix differential equations 总被引:1,自引:0,他引:1
Hai-Jun Peng Zhi-Gang Wu Wan-Xie Zhong 《Journal of Computational and Applied Mathematics》2011,235(12):3571-3588
Combining Fourier series expansion with recursive matrix formulas, new reliable algorithms to compute the periodic, non-negative, definite stabilizing solutions of the periodic Riccati and Lyapunov matrix differential equations are proposed in this paper. First, periodic coefficients are expanded in terms of Fourier series to solve the time-varying periodic Riccati differential equation, and the state transition matrix of the associated Hamiltonian system is evaluated precisely with sine and cosine series. By introducing the Riccati transformation method, recursive matrix formulas are derived to solve the periodic Riccati differential equation, which is composed of four blocks of the state transition matrix. Second, two numerical sub-methods for solving Lyapunov differential equations with time-varying periodic coefficients are proposed, both based on Fourier series expansion and the recursive matrix formulas. The former algorithm is a dimension expanding method, and the latter one uses the solutions of the homogeneous periodic Riccati differential equations. Finally, the efficiency and reliability of the proposed algorithms are demonstrated by four numerical examples. 相似文献