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Sign-changing solutions to second-order integral boundary value problems

✍ Scribed by Yuhua Li; Fuyi Li

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
248 KB
Volume
69
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, by using the fixed point index theory and Leray-Schauder degree theory, we consider the existence and multiplicity of sign-changing solutions to nonlinear second-order integral boundary value problem -u

We obtain some new existence results concerning sign-changing solutions by computing hardly eigenvalues and the algebraic multiplicities of the associated linear problem. If f and g satisfy certain conditions, then this problem has at least six different nontrivial solutions: two positive solutions, two negative solutions and two sign-changing solutions. Moreover, if f and g are also odd, then the problem has at least eight different nontrivial solutions, which are two positive, two negative and four sign-changing solutions.

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This paper concerns the existence of nontrivial solutions for the following singular m-point boundary value problem with a sign-changing nonlinear term is a sign-changing continuous function and may be unbounded from below. By applying the topological degree of a completely continuous field and the