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Abstract: This paper is concerned with the existence of positive solutions of -Laplacian dynamic equation subject to boundary conditions or , where with . By using the five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive solutions. As an application, an example is given to illustrate the result. [Copyright &y& Elsevier]

Abstract: We investigate a class of singular -point -Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential and difference equations , as well as general time scales setting. As an application, an example is given to illustrate the results. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . By the Schauder fixed-point theorem and the upper and lower solution method, we present some existence criteria of the positive solution of m-point singular p-Laplacian dynamic equation with boundary conditions , where with , is continuous for and nonincreasing if . The nonlinear term may be singular in its dependent variable and is allowed to change sign. Our results are new even for the corresponding differential and difference equations . As an application, an example is given to illustrate our result. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . We consider the three-point boundary value problem for -Laplacian dynamic equations on time scales of the form for with boundary conditions , , where is symmetric in and with . By using a pseudo-symmetric technique and the five-functionals fixed-point theorem, we prove that the boundary value problem has at least three positive pseudo-symmetric solutions under some assumptions. As an application, an example is given to illustrate the result. [Copyright &y& Elsevier]

Abstract: In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales where is p-Laplacian operator, i.e., , . Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel''skii''s fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied. [Copyright &y& Elsevier]

Abstract: In this paper, an existence criterion is established for a class of second order perturbed dynamic inclusions on time scales with boundary conditions. The main approach is a fixed-point theorem for multi-valued maps due to Dhage. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that , a i ⩾0 for i =1,…, m −2. Let ξ i satisfy 0< ξ 1 < ξ 2 <⋯< ξ m−2 < ρ(T) and . We consider the following p-Laplacian m-point boundary value problem on time scaleswhere a ∈ C ld ((0, T),[0,∞)) and f ∈ C ld ((0, T)×[0,∞),[0,∞)). Some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems respectively. In particular, our criteria extend and improve some known results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation , , satisfying either the conjugate boundary conditions or the right focal boundary conditions , where a and f are positive. We show that there exists a such that the above boundary value problem has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution of the problem depends continuously on the parameter λ, i.e., is nondecreasing in λ, and . [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . Consider the following three-point boundary value problem on time scales: where , , , , and . By using fixed point theorems in cones, some new and general results are obtained for the existence of single and multiple positive solutions of the above problem. In particular, our criteria generalize and improve some known results. [Copyright &y& Elsevier]