Positive Solutions of a Nonlinear Three-Point Boundary Value Problem on Time Scales

Solutions of Second-Orderm-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales

“…In this section we state the preliminary information that we need to prove the main results. From Lemmas 2.1 and 2.2 in [4], we have the following lemma.…”

“…The theory of dynamic equations on time scales unifies the well-known analogies in the concept of difference equations and differential equations. In the past few years, the boundary value problems of dynamic equations on time scales have been studied by many authors (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references cited therein). Some classical tools have been used in the literature to study dynamic equations.…”

“…These classical tools include the coincidence degree theory [11,12], the method of upper and lower solutions [7,10], and some fixed point theorems in cones for completely continuous operators [1-5, 9, 13-16]. Recently, multiple-point boundary value problems on time scale have been studied for instance [4,5,12].…”

“…By using Green's function and the Leggett-Williams fixed point theorem in an appropriate cone, the existence of at least three positive solutions of the problem is obtained. In 2009, Topal and Yantir [4] studied the general secondorder nonlinear -point boundary value problems:…”

Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

“…In the past few years, the boundary value problems of dynamic equations on time scales have been studied by many authors (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references). Recently, multipoint boundary value problems on time scale have been studied, for instance, see [1][2][3][4][5][6][7][8][9][10][11][12].…”