共查询到20条相似文献,搜索用时 219 毫秒
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A. R. Aliev 《Mathematical Notes》2011,90(3-4):307-321
We obtain sufficient conditions for the regular solvability of initial boundary-value problems for a class of operator-differential equations of third order with variable coefficients on the semiaxis. These conditions are expressed only in terms of the operator coefficients of the equations under study. We obtain estimates of the norms of intermediate derivative operators via the discontinuous principal parts of the equations and also find relations between these estimates and the conditions for regular solvability. 相似文献
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I. P. Ryazantseva 《Russian Mathematics (Iz VUZ)》2013,57(7):45-52
We study equations with multiple-valued operators in a Hilbert space. We understand their solutions in the sense of inclusion. We reduce such equations to mixed variational inequalities or to equations with single-valued operators. For constructed problems we propose implicit iterative processes of the second order and establish sufficient conditions for their strong convergence. 相似文献
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We study linear inhomogeneous vector ordinary differential equations of arbitrary order in which the matrix multiplying the highest derivative of the unknown vector function is singular in the domain where the equations are defined. We also study perturbations (not necessarily small) of such equations, which are linear integro-differential equations with a Volterra operator. We obtain sufficient conditions for the solvability of such equations and give representations of their general solutions; solvability and uniqueness conditions are also given for initial value problems for such equations. The influence of small perturbations of the free term and the initial data on the solution is considered. A numerical method is suggested. The results of numerical experiments are given. 相似文献
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A twist condition and multiple solutions of unbounded self-adjoint operator equation with symmetries
By using the index theory for unbounded self-adjoint operator equations and the symmetric mountain pass theorem, we investigate the existence of multiple solutions for nonlinear operator equations with twist conditions. We prove an abstract theorem, and give some applications to first order Hamiltonian systems with Sturm–Liouville boundary conditions and delay differential equations. 相似文献
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Leon Wejntrob 《Journal of Differential Equations》1977,23(1):162-172
We consider linear differential equations with regular coefficients in . We obtain sufficient conditions for all the solutions of these equations to vanish a given number of times at the most. First the results are obtained for differential equations of second order, then for differential equations of nth order, n > 2. 相似文献
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M. Azizov 《Ukrainian Mathematical Journal》1997,49(9):1299-1304
We propose a direct method for the approximate solution of integral equations that arise in the course of approximate solution of a periodic boundary-value problem for linear differential equations by the method of boundary conditions. We show that the proposed direct method is optimal in order. 相似文献
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In this paper, we consider a class of mathematical programs governed by second-order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict complementarity condition. A set of second order sufficient conditions is proposed, which is proved to be sufficient for the second order growth of the stationary point. The smoothing Newton method in [40] is employed to solve the system of nonsmooth equations whose strongly BD-regularity at a solution point is demonstrated under the second order sufficient conditions. Several illustrative examples are provided and discussed. 相似文献
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In this paper we find conditions that guarantee that regular boundary value problems for elliptic differential-operator equations of the second order in an interval are coercive and Fredholm, and we prove the compactness of a resolvent. We apply this result to find some algebraic conditions that guarantee that regular boundary value problems for degenerate elliptic differential equations of the second order in cylindrical domains have the same properties. Note that considered boundary value conditions are nonlocal and are differential only in their principal part, and a domain is nonsmooth. 相似文献
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Said R. Grace Shurong Sun Yizhuo Wang 《Journal of Applied Mathematics and Computing》2014,44(1-2):119-132
We establish some new criteria for the oscillation of fourth order nonlinear dynamic equations on a time scale. We investigate the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions. Some examples are given here to illustrate our main results. 相似文献
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Boundary Value and Inverse Problems for Some Classes of Nonclassical Operator-Differential Equations
We consider the solvability of boundary value problems and some inverse problems for operator-differential equations of odd order which can be referred to as mixed type equations since the coefficient of the higher order time derivative can change sign. Studying the general classes of boundary value problems with nonlocal boundary conditions, we establish the existence and uniqueness theorems of regular solutions under some conditions on data.
相似文献15.
T. Candan 《Applied Mathematics Letters》2012,25(3):412-416
In this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order nonlinear neutral differential equations. Our results include as special cases some well-known results for linear and nonlinear equations of first, second and higher order. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions. 相似文献
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R Temam 《Journal of Differential Equations》1982,43(1):73-92
We investigate the regularity at time t = 0 of the solutions of linear and semi-linear evolutions equations (including the Stokes and Navier-Stokes equations), Necessary and sufficient conditions on the data for an arbitrary order of regularity are given (the classical “compatibility conditions”). In the case of the Stokes and Navier-Stokes equations the compatibility conditions which we find are global conditions on the data. The presentation given here seems to improve and generalize the known results even in the simplest case of linear evolution equations. 相似文献
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We consider systems of linear differential-algebraic equations of order ≥ 2 and present conditions under which there exist nonsingular transformations splitting the system into systems of linear ordinary differential equations of lower order and, possibly, an algebraic part. 相似文献
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We discuss the solvability of integral equations associated with initial value problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray–Schauder Nonlinear Alternative for several types of initial value problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the “reduction” of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator. 相似文献
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本文研究了高阶复线性微分方程解在角域上的增长性问题.利用Nevanlinna理论和共形变换的方法,获得了一些使得方程非平凡解在角域上有快速增长的系数条件,这些结果丰富了复方程解在角域上增长性的研究. 相似文献
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Tadeusz Jankowski 《Journal of Mathematical Analysis and Applications》2007,332(2):1380-1392
In this paper we deal with second order differential equations with causal operators. To obtain sufficient conditions for existence of solutions we use a monotone iterative method. We investigate both differential equations and differential inequalities. An example illustrates the results obtained. 相似文献