Third-order boundary-value problems for differential equation play a very important role in a variety of different areas of applied mathematics and physics. Recently, third-order boundary-value problems have been many scholars’ research object. For example, heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics can produce boundary-value problems wit...

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: x ′′′ (t) − λ f (t, x) = 0, t ∈ (0, 1); x(0) = x ′ (η) = x ′′ (1) = 0, where 1 2 < η < 1, the non-linear term f (t, x): (0, 1) × (0, +∞) → (−∞, +∞) is continuous and may be singular at t = 0, t = 1...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

The monotone iterative technique, theory of fixed point index in a cone and the Leggett-Williams theorem are applied to investigate existence multiplicity positive solutions for four boundary value problems nonlinear fractional differential equations with p-Laplacian operator infinite delay. Moreover, examples presented illustrate vast applicability our main results.

In this paper, we consider the following dynamic system with parameter on a measure chain T, u i (t) + λhi(t)fi(u1(σ(t)), u2(σ(t)), . . . , un(σ(t))) = 0, t ∈ [a, b], αui(a)− βui (a) = 0, γui(σ(b)) + δui (σ(b)) = 0, where i = 1, 2, . . . , n. Using fixed-point index theory, we find sufficient conditions the existence of positive solutions.

In the case of not requiring the nonlinear term to be monotone or convex, we study the existence of positive solutions for second-order periodic boundary value problem by using the first eigenvalue of the corresponding linear problem and fixed point index theory. The work significantly improves and generalizes the main results of J. Graef et al. [A periodic boundary value problem with vanishing...

By constructing an available integral operator and combining fixed point index theory with properties of Green’s function, this paper shows the existence of multiple positive solutions for a class of impulsive singular boundary value problems with integral boundary conditions. Our results extend some recent work in the literature on boundary value problems of ordinary differential equations. We...

This article concerns the existence and multiplicity of positive solutions for the singular Sturm-Liouville boundary value problem (p(t)u′(t))′ + h(t)f(t, u(t)) = 0, 0 < t <∞, au(0)− b lim t→0+ p(t)u′(t) = 0, c lim t→∞ u(t) + d lim t→∞ p(t)u′(t) = 0. We use fixed point index theory to establish our main results based on a priori estimates derived by utilizing spectral properties of associated l...

In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.