ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO BOUNDARY VALUE PROBLEMS ON TIME SCALES JOHNNY pot

... (1.5). The proofs rely on the a priori bounds on solutions of Section 2 and the nonlinear alternative. The following theorem gives the existence of solutions to the Dirichlet BVP on time scales. Theorem ... (UNSW) and The Australian Research Council’s Discovery Projects (DP0450752). ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO BOUNDA...

Ngày tải lên: 23/06/2014, 00:20

... then (i)–(iv) of Definition 2.5 reduce to the definitions of coerciveness, strong monotonicity, monotonicity, relaxed monotonic- ity, respectively. Obviously, the η-coerciveness implies η-monotonicity. Definit ... the definitions of convexity and st rong convexity, respectively. Remark 2.3. h  is strongly monotone with the constant σ>0ifh is strongly convex with aconstantσ/2...

Ngày tải lên: 22/06/2014, 18:20

... iteration technique, we obtain the local existence of solutions to the Dirichlet initial boundary value problem. We also establish the uniqueness of the solution if the reaction terms satisfy the Lipschitz ... main efforts on the discussion of weak solutions in the sense of the following. Definition 1.1. A nonnegative vector-valued function u =(u 1 ,u...

Ngày tải lên: 21/06/2014, 03:20

... 2.14 As in the proof of Theorem 2.3 we conclude that Tx  x. The proof of uniqueness part is a verbatim repetition of the proof of Theorem 6 in 3. We omit the details. As an application of Theorem ... that the function ϕ satisfies either of the conditions i or ii of Lemma 2.2, then all three theorems Theorems 10, 11, and 12 of 3 can be generalized to...

Ngày tải lên: 21/06/2014, 17:20

... existence and uniqueness of solutions to three-point boundary value problems, ” Journal of Mathematical Analysis and Applications, vol. 167, no. 1, pp. 43–48, 1992. 17 M. Pei and S. K. Chang, Existence ... 2005. 7 Z. Du, W. Ge, and X. Lin, Existence of solutions for a class of third-order nonlinear boundary value problems, ” Journal of Mathematical...

Ngày tải lên: 21/06/2014, 20:20

... point theorem for a class of mixed monotone op- erators, see 6, 14, 18. In virtue of the theorem, we consider the existence and uniqueness of solutions for the following singular higher-order continuous ... continuous and discrete boundary value problems 1.1 and 1.2 by using mixed monotone method. We first discuss the existence and uniqueness of s...

Ngày tải lên: 22/06/2014, 00:20

... point theorem for a class of mixed monotone op- erators, see 6, 14, 18. In virtue of the theorem, we consider the existence and uniqueness of solutions for the following singular higher-order continuous ... continuous and discrete boundary value problems 1.1 and 1.2 by using mixed monotone method. We first discuss the existence and uniqueness of s...

Ngày tải lên: 22/06/2014, 06:20

... 3,wewillobtaininSections4 and 5 the expression of Green’s function and a sufficient condition for the existence and uniqueness of solutions of the dynamic equations of first- and second-order, respectively; ... W n , α and β are a pair of coupled lower and upper solutions of the dynamic equation (L n ) and the function f : I × R → R satisfies hypotheses...

Ngày tải lên: 23/06/2014, 00:20

... know, there is no paper to study the existence of multiple positive solutions to problem 1.1 on time scales with polynomial nonlinearity. The objective of the present paper is to fill this gap. On ... there is a large number of functions that satisfy the conditions of Theorem 3.4. In addition, the conditions of Theorem 3.4 are also easy to check. Ackno...

Ngày tải lên: 21/06/2014, 20:20

... 365–380. [12] J. Henderson, A. Peterson, and C. C. Tisdell, On the existence and uniqueness of solutions to boundary value problems on time scales, AdvancesinDifference Equations 2004 (2004), no. ... just mentioned concern the basic formulation of the linear operator formed from the left-hand side of (1.1), together with the boundar y conditions (1.2),...

Ngày tải lên: 22/06/2014, 22:20