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Zbl 1082.34023
Ma, Ruyun
Existence of positive solutions of a fourth-order boundary value problem. (English)
[J] Appl. Math. Comput. 168, No. 2, 1219-1231 (2005). ISSN 0096-3003

Summary: We consider the fourth-order boundary value problem $$u''''= f(t,u,u''),\ 0<t<1 \quad u(0)=u(1)=u''(0)=u''(1)=0,$$ where $f(t,u,p)= au-bp+o(|(u,p)|)$ near $(0,0)$, and $f(t,u,p)=cu-dp+o(|(u,p)|)$ near $\infty$. We give conditions on the constants $a,b,c,d$ that guarantee the existence of positive solutions. The proof of our main result is based upon global bifurcation techniques.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34C23 Bifurcation (periodic solutions)

Keywords: existence results; eigenvalues; bifurcation methods; positive solutions

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