Three-point Boundary Value Problem Research Articles

Existence Theorem about Triple Positive Solutions for a Boundary Value Problem with p-Laplacian

In this paper, by applying a fixed point theorem to verify the existence of at least three positive solutions to a three-point boundary value problem with p-Laplacian. The interesting point is the nonlinear term is involved with the first-order derivative explicitly.

Existence and uniqueness of monotone positive solutions for a third-order three-point boundary value problem

In this work we study a third-order three-point boundary-value problem (BVP). We derive sucient conditions that guarantee the positivity of the solution of the corresponding linear BVP Then, based on the classi- cal Guo-Krasnosel'skii's fixed point theorem, we obtain positive solutions to the nonlinear BVP. Additional hypotheses guarantee the uniqueness of the solution.

The lower and upper solution method for three-point boundary value problems with integral boundary conditions on a half-line

This paper deal with the following second-order three-point boundary value problem with integral boundary condition on a half-line u''(x) + q(x) f(x, u(x), u'(x)) = 0, x ? (0,+?), u(0) = ? ??0 u(s)ds, u'(+1)=C, where ? > 0, 0 < ?? < 1 and f : [0,+?)x R2 ? R satisfies a Nagumo?s condition which plays an important role in the nonlinear term depend on the first-order derivative explicitly. By using Schauder?s fixed point theorem, the upper and lower solution method and topological degree theory, first we give sufficient conditions for the existence of at least one solution and next at least three solutions of the above problem. Moreover, an example is included to demonstrate the efficiency of the main results.

Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”

Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Existence results for a class of generalized fractional boundary value problems

In this paper, we study a class of generalized fractional order three-point boundary value problems that involve fractional derivative defined in terms of weight and scale functions. Using several fixed point theorems, the existence and uniqueness results are obtained.

Existence of nontrivial solutions for superlinear three-point boundary value problems

In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.

Sequential fractional differential equations with nonlocal boundary conditions on an arbitrary interval

We discuss the existence and uniqueness of solutions for a nonlocal three-point boundary value problem of sequential fractional differential equations on an arbitrary interval [xi, zeta], xi, zetainmathbb{R}. Our results rely on standard fixed point theorems and are well illustrated with examples. The case for non-homogeneous three-point boundary conditions is also discussed.

On some properties of positive solutions for a third-order three-point boundary value problem with a parameter

In this article, we discuss some properties of positive solutions for a third-order differential equation with three-point boundary conditions and a positive parameter. By using recent fixed point theory, we establish the existence and uniqueness of positive solutions for any given parameter, and we show that the positive solution is continuous, increasing with respect to the parameter. Moreover, we give some properties of limits for positive solutions. An example is provided to demonstrate the main result.

Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral

Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral

Recovering a general space-time-dependent heat source by the coupled boundary integral equation method

ABSTRACTAs to recover a time-dependent heat source under an extra temperature measured at an interior point, we can reformulate it to be a three-point boundary value problem. We can develop a coupled boundary integral equation method, wherein by selecting two sets of adjoint test eigenfunctions in two sub domains and using polynomials as the trial functions of unknown heat source, the time-dependent heat source is recovered very well and quickly. Four numerical examples, including a discontinuous one, demonstrate the efficiency for the ill-posed inverse heat source problem in a large time duration and under a large noise up to 10–30%. Then, selecting three sets of adjoint test eigenfunctions in three domains: problem domain and two sub domains, and using the Pascal polynomials as trial functions, the unknown space-time-dependent heat source is recovered very fast and accurately from the solution of three coupled boundary integral equations.

Trajectories reconstruction of spinning baseball pitches by three-point-based algorithm

In this work, a method to reconstruct trajectories by obtaining the initial conditions, velocity and angular velocity, from spinning throws is designed. It is based on considering Magnus effect can be separated from rest of forces that define the dynamics of the ball, such assumption is supported by an energetic analysis. Thus, the methodology consists in solving the two-point boundary value problem (BVP) of the movement equations without Magnus force and then adding its effect.We found that only three points (ball positions as functions of time) of a trajectory are necessary to characterize it, and consequently to solve the three-point BVP. This result is applied in an algorithm based on the shooting method, which obtains the initial conditions of synthetic trajectories by minimizing the distance between points of the original trajectory and those of the proposed trajectory, with high accuracy in a short time.

Applications of measures of noncompactness to infinite system of fractional differential equations

In this paper, we discuss few existence result for solution of an infinite system of fractional differential equations of order ?(1 < ? < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the classical Banach sequence spaces c0 and lp (1 ? p < 1), using Hausdorff measure of noncompactness and Darbo type fixed point theorem. We also illustrate our results through some concrete examples.

Three-point fractional h-sum boundary value problems for sequential Caputo fractional h-sum-difference equations

In this article, we study an existence and uniqueness results for a sequential nonlinear Caputo fractional h-sum-difference equation with three-point fractional h-sum boundary conditions, by using the Banach contraction principle and the Schauder?s fixed point theorem. Our problem contains different orders in three fractional difference operators and three fractional sums. Finally, we provide an example to displays the importance of these results.

Solvability for a system of nonlinear fractional higher-order three-point boundary value problem

Solvability for a system of nonlinear fractional higher-order three-point boundary value problem

Solvability for a system of nonlinear fractional higher-order three-point boundary value problem

Solvability for a system of nonlinear fractional higher-order three-point boundary value problem

Existence and approximation of solution for a nonlinear second-order three-point boundary value problem

A nonlinear second-order ordinary differential equation with four cases of three-point boundary value conditions is studied by investigating the existence and approximation of solutions. First, the integration method is proposed to transform the considered boundary value problems into Hammerstein integral equations. Second, the existence of solutions for the obtained Hammerstein integral equations is analyzed by using the Schauder fixed point theorem. The contraction mapping theorem in Banach spaces is further used to address the uniqueness of solutions. Third, the approximate solution of Hammerstein integral equations is constructed by using a new numerical method, and its convergence and error estimate are analyzed. Finally, some numerical examples are addressed to verify the given theorems and methods.

Existence of positive solutions for second-order impulsive differential equations with delay and three-point boundary value problem

We study the existence of three positive solutions to a type of three-point boundary value problems for second-order impulsive and delay differential equations, and we obtain the result that there exist at least three nonnegative symmetric positive solutions by means of a generalization of the Leggett-Williams fixed point theorem.

A variational approach to perturbed three-point boundary value problems of Kirchhoff-type

In this paper, we provide sufficient conditions for the existence of at least three distinct non-negative weak solutions for a perturbed three-point boundary value problem of Kirchhoff-type. Our technical approach is based on variational methods. In addition, examples are provided to illustrate our results.

Variational principle for a three-point boundary value problem

Variational principle for a three-point boundary value problem