EXISTENCE OF THREE-SOLUTIONS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY VALUE CONDITIONS

摘要

The paper deals with the existence of three-solutions for the second-order differential equations with nonlinear boundary value conditions xn=f(t,x,x'),t∈[a,b],g1(x(a),x'(a))=0,g2(x(b),x'(b))=0,where f:[a,b]×R1×R1→R1,gi:R1×R1→R1(i=1,2)are continuous tunctions. The methods employed are the coincidence degree theory. As an application, the sufficient conditions under which there are arbitrary odd solutions for the BVP are obtained.