共查询到20条相似文献,搜索用时 15 毫秒
1.
K. O. Buryachenko 《Ukrainian Mathematical Journal》2012,63(8):1165-1175
We consider a Cauchy-type boundary-value problem, a problem with three boundary conditions, and the Dirichlet problem for
a general typeless fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a
bounded domain Ω ⊂ R
2 with smooth boundary. By the method of the Green formula, the theory of extensions of differential operators, and the theory
of L-traces (i.e., traces associated with the differential operation L), we establish necessary and sufficient (for elliptic operators) conditions of the solvability of each of these problems
in the space H
m
(Ω), m ≥ 4. 相似文献
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Xuhuan Wang Xiuqing Guo Guosheng Tang 《Journal of Applied Mathematics and Computing》2013,41(1-2):367-375
In this paper, the existence of solutions of an anti-periodic fractional boundary value problem for nonlinear fractional differential equations is investigated. The contraction mapping principle and Leray-Schauder’s fixed point theorem are applied to establish the results. 相似文献
4.
I. V. Skrypnik 《Journal of Mathematical Sciences》1983,21(3):420-427
One introduces a topological characteristic of general nonlinear elliptic problems, one establishes the solvability of the Dirichlet problem for the Monge-Ampere equations and the solvability of the general nonlinear Dirichlet problem in a thin layer. 相似文献
5.
Aruchamy Akilandeeswari Krishnan Balachandran Natarajan Annapoorani 《Journal of Applied Analysis & Computation》2017,7(4):1570-1585
The main purpose of this paper is to study the existence and uniqueness of solutions for the hyperbolic fractional differential equations with integral conditions. Under suitable assumptions, the results are established by using an energy integral method which is based on constructing an appropriate multiplier. Further we find the solution of the hyperbolic fractional differential equations using Adomian decomposition method. Examples are provided to illustrate the theory. 相似文献
6.
Aleksandr L. Pavlov 《Journal of Mathematical Sciences》2014,196(5):665-678
We present sufficient conditions for the existence of solutions of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients and arbitrary boundary data in the space of tempered distributions. 相似文献
7.
Xiangshan Kong Haitao Li Shulan Qin Hongxin Zhao 《Journal of Applied Mathematics and Computing》2017,54(1-2):81-93
This paper studies the bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations with parameter. Using the topological degree theory and the bifurcation technique, the existence of positive solutions is investigated and some sufficient conditions are obtained. The study of two illustrative examples shows that the obtained new results are effective. 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
11.
Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations 总被引:1,自引:0,他引:1
In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. 相似文献
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We consider the solvability of a boundary-value problem of form (1), (2) in the class of nonlinearities of f, for which the traditional restrictions of the Lifschitz-conditions type are replaced by concavity (or generalized concavity) conditions with respect to specially chosen variables.Senior Lecturer.Candidate of Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 700–703, May, 1992. 相似文献
14.
Yige Zhao 《Journal of Applied Analysis & Computation》2018,8(4):1170-1185
In this paper, we consider the existence of positive solutions for a class of nonlinear singular fractional differential systems with multi-orders. Our analysis relies on fixed point theorems on cones. Some sufficient conditions for the existence of at least one or two positive solutions for boundary value problem of nonlinear singular fractional differential systems with multi-orders are established. As an application, an example is presented to illustrate the main results. 相似文献
15.
In this paper, we investigate the solvability of infinite-point boundary value problems for a class of higher-order factional differential equations on the half-line involving Riemann–Liouville derivatives. Under a new compactness criterion, some new results are obtained by means of the properties of the Green’s function and some appropriate fixed point theorems on cone. 相似文献
16.
N. Nyamoradi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(4):145-157
The paper studies the problem of existence of positive solution to the following boundary value problem: $D_{0^ + }^\sigma u''(t) - g(t)f(u(t)) = 0$ , t ∈ (0, 1), u″(0) = u″(1) = 0, au(0) ? bu′(0) = Σ i=1 m?2 a i u(ξ i ), cu(1) + du′(1) = Σ i=1 m?2 b i u(ξ i ), where $D_{0^ + }^\sigma$ is the Riemann-Liouville fractional derivative of order 1 < σ ≤ 2 and f is a lower semi-continuous function. Using Krasnoselskii’s fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is established. 相似文献
17.
This paper is devoted to proving the existence and uniqueness of solutions to Cauchy type problems for fractional differential equations with composite fractional derivative operator on a finite interval of the real axis in spaces of summable functions. An approach based on the equivalence of the nonlinear Cauchy type problem to a nonlinear Volterra integral equation of the second kind and applying a variant of the Banach’s fixed point theorem to prove uniqueness and existence of the solution is presented. The Cauchy type problems for integro-differential equations of Volterra type with composite fractional derivative operator, which contain the generalized Mittag-Leffler function in the kernel, are considered. Using the method of successive approximation, and the Laplace transform method, explicit solutions of the open problem proposed by Srivastava and Tomovski (2009) [11] are established in terms of the multinomial Mittag-Leffler function. 相似文献
18.
In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results. 相似文献
19.
In this paper, by using the Schauder fixed point theorem, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and obtain some new results. 相似文献
20.
This article gives an exposition of the fundamental results of the theory of boundary-value problems for ordinary second-order differential equations having singularities with respect to the independent variable or one of the phase variables. In particular criteria are given for solvability and unique solvability of two-point boundary-value problems and problems concerning bounded and monotonic solutions. Several specific problems are considered which arise in applications (atomic physics, field theory, boundary-layer theory of a viscous incompressible fluid, etc.)Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 30, pp. 105–201, 1987. 相似文献