An existence and uniqueness result concerned with the boundaryvalueproblem u " + g(t, u(t)) = e(t), u'(0) = u'(pi) = 0 is presented. (C) 2000 Academic Press.
An existence and uniqueness result concerned with the boundaryvalueproblem u " + g(t, u(t)) = e(t), u'(0) = u'(pi) = 0 is presented. (C) 2000 Academic Press.
In this paper, we consider the following boundaryvalueproblem: { ((-u'(t))(n))' = nt (n-1) f(u(t)) for 0 1. Using the fixed point theory on a cone and approximation technique, we obtain the existence of pos...
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In this paper, we consider the following boundaryvalueproblem: { ((-u'(t))(n))' = nt (n-1) f(u(t)) for 0 < t < 1, u'(0) = 0, u(1) = 0, where n > 1. Using the fixed point theory on a cone and approximation technique, we obtain the existence of positive solutions in which f may be singular at u = 0 or f may be sign-changing.
two-point boundary value problem for fourth order partial integro-differential equation is considered. By new unknown function the problem is reduced to an equivalent family of two-point boundary value problems for th...
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two-point boundary value problem for fourth order partial integro-differential equation is considered. By new unknown function the problem is reduced to an equivalent family of two-point boundary value problems for the Volterra integro-differential equations of second order. By the method of introduction functional parameters are constructed the algorithms for finding of solution to family of two-point boundary value problems for the Volterra integro-differential equations of second order. Conditions of existence unique solution to family of two-point boundary value problems for Volterra integro-differential equations of second order are obtained in the terms of initial data. Criteria of unique solvability to the two-point boundary value problem for fourth order partial integro-differential equation is established.
We consider the existence of multiple positive solutions of a nonlinear two-point boundary value problem by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the number of positive...
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A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution ...
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A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution for Q ≥ 0. This improves a recent result that theproblem has at least one solution for 0 ≤ Q ≤ 13.21.
High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative ...
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High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved.
By using partial order method. some existing theorems of solutions for two-point bouniary valueproblem of second order ordinary differenlial equations in Banach spaces are given.
By using partial order method. some existing theorems of solutions for two-point bouniary valueproblem of second order ordinary differenlial equations in Banach spaces are given.
In this article, we consider the motion of a liquid surface between two parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact b...
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In this article, we consider the motion of a liquid surface between two parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact between a capillary surface and a solid surface takes values in a closed interval. Furthermore, the evolution of the contact angle as a function of the contact area exhibits hysteresis. We study the two-point boundary value problem in time whereby a liquid surface with one contact angle at t = 0 is deformed to another with a different contact angle at t = infinity while the volume remains constant, with the goal of determining the energy loss due to viscosity. The fluid flow is modeled by the Navier-Stokes equations, while the Young-Laplace equation models the initial and final capillary surfaces. It is well-known even for ordinary differential equations that two-point boundary value problems may not have solutions. We show existence of classical solutions that are non-unique, develop an algorithm for their computation, and prove convergence for initial and final surfaces that lie in a certain set. Finally, we compute the energy lost due to viscous friction by the central solution of the two-point boundary value problem.
Using Leray-Schauder fixed point theorem, the solvability was considered for a singular second-order two-point boundary value problem with first order derivative. The main conditions of results are local. In other wor...
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Using Leray-Schauder fixed point theorem, the solvability was considered for a singular second-order two-point boundary value problem with first order derivative. The main conditions of results are local. In other words, the problem must have a solution or positive solution provided that the height of principal part of the nonlinear term is appropriate on a bounded subset of its domain.
In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which relate first and second spatial derivatives at the boundarypoints. ...
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In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which relate first and second spatial derivatives at the boundarypoints. Moreover, the unique solution to this problem can be represented probabilistically in terms of a sticky Brownian motion. This probabilistic representation is attained from the stochastic differential equation for a sticky Brownian motion on the bounded interval [0,1].
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