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Zbl 1111.34019
Han, Guodong; Wu, Ying
Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms. (English)
[J] J. Math. Anal. Appl. 325, No. 2, 1327-1338 (2007). ISSN 0022-247X

Summary: The singular two-point boundary value problem $$-u''(t)=h(t)f(u(t),\ t\in(0,1);\quad u(0)=u(1)=0,$$ is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear problem, where $h$ is allowed to be singular at both $t=0$ and $t=1$. Moreover, $f:(-\infty,+\infty) \to(-\infty,+\infty)$ is a sign-changing function and not necessarily bounded from below. By computing the topological degree of an completely continuous field, existence results for nontrivial solutions are established.

MSC 2000:: *34B16 Singular nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: singular boundary value problems; nontrivial solution; cone; Leray-Schauder degree

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