On the existence of positive solutions of nonlinear second order differential equations

Lian, Wei-Cheng; Wong, Fu-Hsiang; Yeh, Cheh-Chih

doi:10.1090/S0002-9939-96-03403-X

On the existence of positive solutions of nonlinear second order differential equations
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by Wei-Cheng Lian, Fu-Hsiang Wong and Cheh-Chih Yeh PDF

Proc. Amer. Math. Soc. 124 (1996), 1117-1126 Request permission

Abstract:

Under suitable conditions on $f(t,u)$, the boundary value problem \begin{equation*} \begin {cases} (E)~~ u''(t)+f(t,u(t))=0~~~~~\mathrm {in}~~~~~(0,1),\ (BC) \begin {cases} \alpha u(0)-\beta u’(0)=0,\ \gamma u(1)+\delta u’(1)=0\end{cases} \end{cases} \tag *{(BVP)} \end{equation*} has at least one positive solution. Moreover, we also apply this main result to establish several existence theorems of multiple positive solutions for some nonlinear (elliptic) differential equations.

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