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1.
Existence results for partial neutral functional integrodifferential equations with unbounded delay 总被引:1,自引:0,他引:1
Eduardo Hernández 《Journal of Mathematical Analysis and Applications》2004,292(1):194-210
We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative. 相似文献
2.
Eduardo Hernández M. Marco Rabello 《Journal of Mathematical Analysis and Applications》2007,331(2):1135-1158
This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations. 相似文献
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4.
The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation
with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic
optimal control. 相似文献
5.
We prove the existence of solutions for some semilinear elliptic equations in the appropriate H4 spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results. 相似文献
6.
Seyedeh Marzieh Ghavidel 《Journal of Mathematical Analysis and Applications》2008,345(2):854-870
We investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations , t?s, us=φ, where B(t) is a family of nonlinear multivalued, α-accretive operators with D(B(t)) possibly depending on t, and the operators F(t,.) being defined—and Lipschitz continuous—possibly only on “thin” subsets of the initial history space E. The results are applied to population dynamics models. We also study the asymptotic behavior of solutions to this equation. Our analysis will be based on the evolution operator associated to the equation in the initial history space E. 相似文献
7.
Najja S. Al-Islam 《Applied mathematics and computation》2012,218(11):6536-6548
In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed. 相似文献
8.
Ciprian G. Gal 《Journal of Mathematical Analysis and Applications》2007,333(2):971-983
In this paper we consider the nonlinear differential equation with deviated argument u′(t)=Au(t)+f(t,u(t),u[φ(u(t),t)]), t∈R+, in a Banach space (X,‖⋅‖), where A is the infinitesimal generator of an analytic semigroup. Under suitable conditions on the functions f and φ, we prove a global existence and uniqueness result for the above equation. 相似文献
9.
Nguyen Dinh Phu Le Thanh Quang Tran Thanh Tung 《Nonlinear Analysis: Theory, Methods & Applications》2008
The existence and comparison results on solutions of set control differential equation were studied in [N.D. Phu, T.T. Tung, Some results on sheaf-solutions of sheaf set control problems, Nonlinear Analysis 67 (2007) 1309–1315]. In this paper, we present the stability criteria for solutions of set control differential equation. 相似文献
10.
Robert C. Dalang Olivier Lé vê que 《Transactions of the American Mathematical Society》2006,358(5):2123-2159
We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.
11.
Tomomi Yokota 《Journal of Mathematical Analysis and Applications》2011,380(2):455-466
Global existence and smoothing effect are established for the complex Ginzburg-Landau type equation in which the real and imaginary parts of the complex coefficient are multiplied by nonlinear terms with different powers. The proof is based on monotonicity methods described by subdifferential operators. The key lies in two modified inequalities. 相似文献
12.
We study the existence of W2,1 solutions for singular and nonsmooth initial value problems of the type whereT > 0 is a priori fixed, x0, x1 ∈ ?, and F: [0, T ] × ? → ??(?) \ {??} is a multivalued mapping. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Andreas Johann 《Journal of Differential Equations》2002,184(1):224-258
We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions. 相似文献
14.
Waldemar Pompe 《Mathematical Methods in the Applied Sciences》2004,27(11):1347-1365
We find a common abstract formulation of the quasistatic and dynamic problems from viscoplasticity theory. Based on this formulation we show existence and uniqueness of the solution to this abstract problem by choosing appropriate spaces and by reducing the problem to an evolution equation, which can be treated by the general theory of monotone operators in Hilbert space. Our proof is valid for non‐linearities in the constitutive equation with power law growth. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
Massimo Gobbino 《Mathematical Methods in the Applied Sciences》1999,22(5):375-388
We investigate the evolution problem where H is a Hilbert space, A is a self‐adjoint linear non‐negative operator on H with domain D(A), and is a continuous function. We prove that if , and , then there exists at least one global solution, which is unique if either m never vanishes, or m is locally Lipschitz continuous. Moreover, we prove that if for all , then this problem is well posed in H. On the contrary, if for some it happens that for all , then this problem has no solution if with β small enough. We apply these results to degenerate parabolic PDEs with non‐local non‐linearities. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
16.
In this article, we discuss the existence of multiple solutions to a one-dimensional stochastic differential delay equation with continuous drift coefficients and derive a related comparison theorem. 相似文献
17.
Fuensanta Andrs Julio Muoz Jesús Rosado 《Mathematical Methods in the Applied Sciences》2019,42(18):6049-6066
This work is a follow‐up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal optimal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state equation, a detailed formulation of the nonlocal optimal design is given. The state equation is of nonlocal parabolic type, and the associated cost functional belongs to a broad class of nonlocal integrals. In the first part of the work, a general result on the existence of nonlocal optimal design is proved. The second part is devoted to analyzing the convergence of nonlocal optimal design problems toward the corresponding classical problem of optimal design. After a slight modification of the problem, either on the cost functional or by considering a new set of admissibility, the G‐convergence for the state equation and, consequently, the convergence of the nonlocal optimal design problem are proved. 相似文献
18.
In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated. 相似文献
19.
Josep M. Olm Xavier Ros-Oton Tere M. Seara 《Journal of Mathematical Analysis and Applications》2011,381(2):582-589
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x?x−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied. 相似文献
20.
We establish the existence of bounded, almost periodic and asymptotically almost periodic mild solutions for first- and second-order abstract-retarded functional differential equations with unbounded delay. 相似文献