Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10427007 | Nonlinear Analysis: Theory, Methods & Applications | 2005 | 10 Pages |
Abstract
The existence of n and infinitely many positive solutions is proved for the nonlinear fourth-order periodic boundary value problemu(4)(t)-βuâ²â²(t)+αu(t)=f(t,u(t)),0⩽t⩽1,u(i)(0)=u(i)(1),i=0,1,2,3,where n is an arbitrary natural number and β>-2Ï2,0<α<(12β+2Ï2)2,α/Ï4+β/Ï2+1>0. This kind of fourth-order boundary value problems usually describes the equilibrium state of an elastic beam with periodic boundary condition. The main results show that the problem may have n or infinitely many positive solutions provided the growth rates of nonlinear term f(t,l) are appropriate on some bounded subsets of its domain.
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Authors
Qingliu Yao,