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Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms. (English) Zbl 1111.34019
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.

34B16Singular nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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