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

     

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.     

Solvability of Sturm-Liouville problems on time scales at resonance

Under the appropriate growth conditions on the inhomogeneous term, we present the existence of the nontrivial solution for Sturm-Liouville boundary value problems on time scales at resonance by making use of coincidence degree theory of Mawhin. The interesting point is the nonlinearity f which is involved with first-order Δ-derivative explicitly.     

Positive solution for system of nonlinear first-order PBVPs on time scales

In this paper we are concerned with the following system of nonlinear first-order periodic boundary value problems on time scale $\mathbb{T}$where $f_i:[0,T]\times [0,+\infty {)}^n\to \mathbb{R}$ is continuous and there exists a constant $M_i>0$ such that$M_i{x}_i-f_i(t,x_1,x_2,\dots ,x_n)⩾0\text{for}(x_1,x_2,\dots ,x_n)\in [0,+\infty {)}^n,t\in [0,T]\text{.}$Some existence criteria of positive solution are established by using a fixed point theorem for operators on cone.     

Positive solutions and eigenvalue regions of two-delay singular systems with a twin parameter

The paper is concerned with a two-delay singular differential system with a twin parameter. Applying fixed-point index theory, we show the relationship between the asymptotic behaviors of nonlinearities (at zero and infinity) and the open regions (eigenvalue regions) of parameters, which are correlated with delays, such that the system has zero, one and two positive solution(s).     

Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales

In this paper, by using critical point theory, we establish the existence of weak solutions of the two-point boundary value problem for a second-order dynamic equation on an arbitrary time scale T$\mathbb{T}$, so that the well known case of differential dynamic systems (T=R)$(\mathbb{T}=\mathbb{R})$ and the recently developed case of discrete dynamic systems (T=Z)$(\mathbb{T}=\mathbb{Z})$ are unified. To the best of our knowledge, this is the first time that boundary value problems of dynamic equations on time scales have been dealt with by using critical point theory.     

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.     

Interval criteria for oscillation of nonlinear second-order dynamic equations on time scales

Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and an integral averaging technique. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.