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Abstract: This paper deals with a class of boundary value problem of singular differential equations on time scales. The conditions we used here differ from those in the majority of papers as we know. An existence theorem of positive solutions is established by using the Krasnosel''skii fixed point theorem and an example is given to illustrate it. [Copyright &y& Elsevier]

Abstract: In this work a general class of nonlinear abstract equations satisfying a generalized strong maximum principle is considered in order to study the behavior of the bounded components of positive solutions bifurcating from the curve of trivial states at a nonlinear eigenvalue with geometric multiplicity one. Since the unilateral theorems of Rabinowitz (J. Funct. Anal. 7 (1971) 487, Theorems 1.27 and 1.40) are not true as originally stated (cf. the very recent counterexample of Dancer, Bull. London Math. Soc. 34 (2002) 533), in order to get our main results the unilateral theorem of López-Gómez (Spectral Theory and Nonlinear Functional Analysis, Research Notes in Mathematics, vol. 426, CRC Press, Boca Raton, FL, 2001, Theorem 6.4.3) is required. Our analysis fills some serious gaps existing is some published papers that were provoked by a direct use of Rabinowitz''s unilateral theory. Actually, the abstract theory developed in this paper cannot be covered with the pioneering results of Rabinowitz (1971), since in Rabinowitz''s context any component of positive solutions must be unbounded, by a celebrated result attributable to Dancer (Arch. Rational Mech. Anal. 52 (1973) 181). [Copyright &y& Elsevier]

Abstract: In this paper, we consider the following p-Laplacian multipoint boundary value problem on time scales:where , , , . By using fixed point index, we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. Especially, the nonlinear term is allowed to change sign. As an application, an example is given to demonstrate our result. [Copyright &y& Elsevier]

Abstract: In this paper, the three-point boundary value problem and its conjugate boundary value problem are studied under some conditions concerning the same first eigenvalue of the both linear problems. By applying the fixed point index theory, the coexistence of single and multiple positive solutions of the above mentioned problems is verified. As an application, some examples are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation , , subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems. [Copyright &y& Elsevier]

Abstract: This paper presents a variety of existence results for nonlinear multi-point boundary value problem on the half-line. In particular, we consider Existence results are established using fixed-point theorems on cone. [Copyright &y& Elsevier]

Abstract: In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones. [Copyright &y& Elsevier]

Abstract: In this paper, we study a class of superlinear semipositone singular second order Dirichlet boundary value problem. A sufficient condition for the existence of positive solution is obtained under the more simple assumptions. [Copyright &y& Elsevier]

Abstract: This paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one-dimensional p-Laplacian differential equation , subject to some boundary conditions. We show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence of positive solutions of the equation where is an increasing homeomorphism and homomorphism and , subject to linear mixed boundary conditions by a simple application of a fixed point index theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the problem of existence of positive solutions for the nonlinear singular third-order three-point boundary value problem where λ is a positive parameter and is a constant. By using a fixed point theorem of cone expansion-compression type due to Krasnosel''skii, we establish various results on the existence of single and multiple positive solutions to the boundary value problem. Under various assumptions on functions F and a, we give explicitly the intervals for parameter λ in which the existence of positive solutions is guaranteed. Especially, we allow the function of nonlinear term to have suitable singularities. [Copyright &y& Elsevier]

Abstract: In this paper, we characterize the eigenvalues and show existence of positive solutions to discrete boundary value problem (here , and is a parameter) [Copyright &y& Elsevier]

Abstract: Usually we do not think there is variational structure for singular elliptic boundary value problems, so it cannot be considered by using critical points theory. In this paper, we use critical theory on certain convex closed sets to solve positive solutions for singular elliptic boundary value problems, especially use the ordinary differential equation theory of Banach spaces to obtain new results on the existence of multiple positive solutions. The method is useful for other singular problems. [Copyright &y& Elsevier]