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Abstract: An -point boundary value problem with one-dimensional -Laplacian at resonance on is considered. By establishing a continuation theorem and applying a suitable homotopy, Leray–Schauder degree, a priori estimate, the existence of solutions to the above problem is obtained. [Copyright &y& Elsevier]

Abstract: This paper studies the existence of nontrivial solutions for a class of higher-order m-point singular boundary value problems based on the topological degree of a completely continuous field, the first eigenvalue and its corresponding eigenfunction of a special linear operator. The nonlinear term in the boundary value problems is sign-changing and may be unbounded from below. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the existence of single and multiple solutions of three-point boundary value problems for the following nonlinear singular second-order differential equations where , is continuous and may be singular at , is continuous and may take a negative value. By applying the technique of lower and upper solutions and the theory of topological degree, we obtain the conditions for the existence of at least one solution and at least three solutions respectively. [Copyright &y& Elsevier]

This paper investigates the following singular systems of nonlinear second-order three-point boundary value problems where , and may be singular at and/or . Under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression. Two examples are then presented to demonstrate the application of our main results. [Copyright &y& Elsevier]