Existence, multiplicity and infinite solvability of positive solutions to a nonlinear fourth-order periodic boundary value problem

✍ Scribed by Qingliu Yao

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 179 KB
• Volume: 63
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.05.009

✦ Synopsis

The existence of n and infinitely many positive solutions is proved for the nonlinear fourth-order periodic boundary value problem

where n is an arbitrary natural number and > -2 2 , 0 < < ( 1 2 + 2 2 ) 2 , / 4 + / 2 + 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.