Bifurcation from interval and positive solutions for a class of fourth-order two-point boundary value problem

摘要

We consider the fourth-order two-point boundary value problem x ′′′′ + k x ″ + l x = f ( t , x ) , 0 t 1 , x ( 0 ) = x ( 1 ) = x ′ ( 0 ) = x ′ ( 1 ) = 0 , which is not necessarily linearizable. We give conditions on the parameters k, l and f ( t , x ) that guarantee the existence of positive solutions. The proof of our main result is based upon topological degree theory and global bifurcation techniques. MSC:34B15.