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Abstract: This paper investigates an -point boundary value problem with nonlinear boundary conditions at resonance on infinite intervals. By establishing a general continuation theorem, the existence and uniqueness of unbounded solutions is obtained on the basis of a suitable homotopy, Leray–Schauder degree properties and a priori estimate. This paper provides a new method to solve boundary value problems with nonlinear boundary conditions at resonance on infinite intervals. [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: The existence and multiplicity of unbounded solutions is investigated for second-order three-point differential equations with nonlinear boundary conditions on , where the growth of the nonlinear term with respect to the third variable is allowed to be quadratic. By applying the techniques of unbounded upper and lower solutions and the topological degree theory, the existence of at least one solution and three solutions, respectively, is shown for the above problem. One example is worked out to indicate the applications of our main results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the existence of nontrivial periodic solutions to the following nonlinear differential equation where is an -periodic continuous function with is continuous, may take negative values and can be sign-changing. Without making any nonnegative assumption on nonlinearity, by using the first eigenvalue corresponding to the relevant linear operator and the topological degree, the existence of nontrivial periodic solutions to the above periodic boundary value problem is established. Finally, three examples are given to demonstrate the validity of our main results. [Copyright &y& Elsevier]

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]