Positive solutions for a class of semipositone periodic boundary value problems via bifurcation theory

He, Zhiqian and Ma, Ruyun and Xu, Man: Positive solutions for a class of semipositone periodic boundary value problems via bifurcation theory. Electronic journal of qualitative theory of differential equations 29. pp. 1-15. (2019)

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Abstract

In this paper, we are concerned with the existence of positive solutions of nonlinear periodic boundary value problems like − u 00 + q(x)u = λ f(x, u), x ∈ (0, 2π), u(0) = u(2π), u 0 (0) = u 0 (2π), where q ∈ C([0, 2π], [0, ∞)) with q 6≡ 0, f ∈ C([0, 2π] × R+, R), λ > 0 is the bifurcation parameter. By using bifurcation theory, we deal with both asymptotically linear, superlinear as well as sublinear problems and show that there exists a global branch of solutions emanating from infinity. Furthermore, we proved that for λ near the bifurcation value, solutions of large norm are indeed positive.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 29
Page Range: pp. 1-15
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.29
Uncontrolled Keywords: Határérték probléma - differenciálegyenletek, Bifurkációelmélet
Additional Information: Bibliogr.: p. 14-15. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 27. 12:02
Last Modified: 2019. Sep. 27. 13:22
URI: http://acta.bibl.u-szeged.hu/id/eprint/62107

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