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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.

MSC:
34B16Singular nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
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References:
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