Existence of positive solutions for nonlinear three-point problems on time scales

In this paper, by using fixed point theorems in cones, we study the existence of at least one, two and three positive solutions of a nonlinear second-order three-point boundary value problem for dynamic equations on time scales. As an application, we also give some examples to demonstrate our results.     

Existence of solutions for a first-order p-Laplacian BVP on time scales

We introduce a first-order delta dynamic equation on time scales involving the one-dimensional p$p$-Laplacian, and prove the existence of at least one positive solution. An example applying our result is also given.     

Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales

In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales

     

Oscillatory criteria for third-order nonlinear difference equation with impulses

In this paper, we study the oscillation of a third-order nonlinear difference equation with impulses. Some sufficient conditions for the oscillatory behavior of solutions of third-order impulsive nonlinear difference equation are obtained. Some known results in the literature are generalized and improved.     

Three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations

In this paper, we consider the existence of at least three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations. The associated Green’s function for the boundary value problems is first given. The proofs of our main results are based upon the Leggett–Williams fixed point theorem. Finally, we give an example to demonstrate our result.     

Existence of a positive almost periodic solution for a nonlinear delay integral equation

In this paper, we discuss the existence of positive almost periodic solution for some nonlinear delay integral equation, by constructing a new fixed point theorem in the cone. Some known results are extended.     

The mixed BVP for second order nonlinear ordinary differential equation at resonance

Efficient sufficient conditions are established for the solvability of the mixed problem where in the case where the homogeneous linear problem has nontrivial solutions.     

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented.     

EXISTENCE OF POSITIVE SOLUTIONS AND 1／c-GLOBAL ATTRACTIVITY OF A NONLINEAR DELAY DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

Abstract. The existence of positive solutions and the global attractivity of the difference equa-tion