In this article, some new sufficient conditions are obtained by making use of fixed point index theory in cone and constructing some available integral operators together with approximating technique. They guarantee t...
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In this article, some new sufficient conditions are obtained by making use of fixed point index theory in cone and constructing some available integral operators together with approximating technique. They guarantee the existence of at least one positive solution for nonlinear fourth-order semipositone multi-point boundary value problems. The interesting point is that the nonlinear term f not only involve with the first-order and the second-order derivatives explicitly, but also may be allowed to change sign and may be singular at t = 0 and/or t = 1. Moreover, some stronger conditions that common nonlinear term f a parts per thousand yen 0 will be modified. Finally, two examples are given to demonstrate the validity of our main results. 2000 Mathematics Subject Classification: 34B10;34B18;47N20.
In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. A...
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In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results.
Purpose - multi-point boundary value problems have important. roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of ordinary differential equations with mult...
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Purpose - multi-point boundary value problems have important. roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of ordinary differential equations with multi-pointboundaryvalue conditions by means of a semi-numerical approach which is based on the homotopy analysis method. Design/methodology/approach - The convergence of the obtained solution is expressed and some typical examples are employed to illustrate validity, effectiveness and flexibility of this procedure. This approach, in contrast to perturbation techniques, is valid even for systems without any small/large parameters and therefore it can be applied more widely than perturbation techniques, especially when there do not exist any small/large quantities. Findings - Unlike other analytic techniques, this approach provides a convenient way to adjust and control the convergence of approximation series. Some applications will be briefly introduced. Originality/value - The paper shows how an important boundaryvalue problem is solved with a semi-analytical method.
We consider optimal two-impulse space interception problems with multiple *** multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitu...
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We consider optimal two-impulse space interception problems with multiple *** multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity *** optimization problems are formulated as multi-point boundary value problems and solved by the calculus of *** variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is *** a result,an indirect optimization method is ***,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical ***,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.
In this article, multi-pointboundaryvalue systems with impulsive effects are considered. Existence of at least one classical solution is investigated. The basis of the approach is an application of certain variation...
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In this article, multi-pointboundaryvalue systems with impulsive effects are considered. Existence of at least one classical solution is investigated. The basis of the approach is an application of certain variational methods for smooth functionals, which are defined on reflexive Banach spaces. Examples are provided in order to illustrate how the presented results can be applied.
In this article, we discuss the nonlinear multi-point boundary value problems for second order impulsive differential equations. Some sufficient conditions for the existence and nonexistence of positive solutions are ...
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In this article, we discuss the nonlinear multi-point boundary value problems for second order impulsive differential equations. Some sufficient conditions for the existence and nonexistence of positive solutions are proposed by using fixed point theorem in a cone.
This paper introduces the improved LS-SVM algorithms for solving two-point and multi-point boundary value problems of high-order linear and nonlinear ordinary differential equations. To demonstrate the reliability and...
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This paper introduces the improved LS-SVM algorithms for solving two-point and multi-point boundary value problems of high-order linear and nonlinear ordinary differential equations. To demonstrate the reliability and powerfulness of the improved LS-SVM algorithms, some numerical experiments for third-order, fourth-order linear and nonlinear ordinary differential equations with two-point and multi-pointboundary conditions are performed. The idea can be extended to other complicated ordinary differential equations.
We study the nonlinear boundaryvalue problem consisting of the equation y '' + w(t)f(y) = 0 on [a, b] and a multi-pointboundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville proble...
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We study the nonlinear boundaryvalue problem consisting of the equation y '' + w(t)f(y) = 0 on [a, b] and a multi-pointboundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes in the existence question for different types of nodal solutions as the problem changes. (C) 2009 Elsevier Ltd. All rights reserved.
In this work, a singularly perturbed second-order ordinary differential equation is solved by applying a new Liouville-Green transform and the asymptotic solutions are obtained. As an application, we employ our result...
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In this work, a singularly perturbed second-order ordinary differential equation is solved by applying a new Liouville-Green transform and the asymptotic solutions are obtained. As an application, we employ our results in discussing a second-order multi-pointboundaryvalue problem. (C) 2010 Elsevier Ltd. All rights reserved.
This paper deals with the existence of multiple positive solutions for multi-point boundary value problems with p-Laplacian on infinite intervals. By using three fixed point theorems in cones, especially a five functi...
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This paper deals with the existence of multiple positive solutions for multi-point boundary value problems with p-Laplacian on infinite intervals. By using three fixed point theorems in cones, especially a five functionals fixed point theorem, we obtain the sufficient conditions for the existence of at least one, two and three positive solutions, respectively. Two examples are also given in this paper to illustrate the main results.
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