[PDF] Top 20 On the Solvability of Nonlinear Boundary Value Problems on Time Scales

... I am grateful for the help of Miriam Ansley, Seyma Bennett-Shabbir, Di Bucklad, Brenda Currin, Carolyn Gunton, Nicole Newkirk Dahlke, Marilyn McCollum, Denise Seabrooks, and Charlene Wallace during my time at NC ... See full document

... This paper is concerned with the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of an elastic beam which is acted upon by axi[r] ... See full document

... There is an ongoing flurry of research activities devoted to positive solutions of dy- namic equations on time scales (see, e.g., [1–7]). This work entails an extension of the paper by Chyan and Henderson ... See full document

... integral boundary value problems on time scales at resonance, this paper will establish some sufficient conditions for the existence of at least one solution to BVPs ... See full document

... the boundary value problems on time scales, often using Guo-Krasnosel’skii fixed point ...of nonlinear boundary value problems on time scales; ... See full document

... Proof. This is a special case of Lloyd [15, Theorem 4.4.11]. Recently the study of dynamic equations on time scales has attracted much interest (see [1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14]). This has been ... See full document

... suitable boundary value problems are obtained and the differences and the similarities between the discrete and the continuous problems are pointed ... See full document

... By using the classical fixed point theorem for operators on cone, in this article, some results of one and two positive solutions to a class of nonlinear first-order periodic boundary value ... See full document

... multipoint boundary value problems arise in a variety of different areas of applied mathematics and ...multipoint boundary value problem 2; also many problems in the theory of ... See full document

... Time scales and time-scale notation are introduced well in the fundamental texts by Bohner and Peterson 1, 2 , respectively, as important ...of boundary value problems on ... See full document

... a boundary value problem and, indeed, it has received considerable ...general time scales, there are certain difficulties with this basic ...the time scale, but we show that these ... See full document

... The rest of this paper is organized as follows. Section 2 contains some necessary notations, definitions, and lemmas. In Section 3, we establish a theorem on existence of solutions for BVP (1.1) under nonlinear ... See full document

... periodic boundary value problems PBVPs for short for dynamic equations on time scales have been studied by several authors by using the method of lower and upper solutions, fixed point ... See full document

... Assume that T has a topology that it inherits from the standard topology on R and define the time scale interval 0, 1 T {t ∈ T : 0 ≤ t ≤ 1}. For t ∈ T, define the forward jump operator σ : T → T by σt inf{s ∈ T : ... See full document

... The main features in this paper are as follows. First, we study two new multi-point BVPs on time scales at resonance, which have rarely been considered, and thus we need to over- come some new difficulties. ... See full document

... a time scale defined as the real numbers set, and in the second one, the existence of extremal solutions to PBVP ...a time scale defined as a sequence of discrete points union a closed real interval is ... See full document

... As far as we 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. ... See full document

... Sturm-Liouville boundary value problems (for short BVPs) have received a lot of ...Dirichlet boundary conditions [, ...Sturm-Liouville boundary value problems with ... See full document

... on time scales, which has been cre- ated in order to unify the study of differential and difference equations, is an area of math- ematics that has recently received a lot of attention; moreover, many results ... See full document

... Semipositone problems arise in bulking of mechanical systems, design of suspension bridges, chemical reactions, astrophysics, combustion, and management of natural ... See full document