A New Solution Operator of One-Dimensionalp-Laplacian with a Sign-Changing Weight and Its Application

摘要

We establish a new solution operator for the following problem-φp(u′)′=g,t∈(0,1),u(0)=0=u(1), whereφp(x)=|x|p-2x,p>1.gmay be singular at the boundary or change signs or may not be inL1(0,1)so that this solution operator can cover larger class ofgthan previously known ones. As an application, by checking complete continuity of the solution operator, we show the existence of nontrivial solutions forp-Laplacianφp(u′)′+λh(t)f(u(t))=0,t∈(0,1),u(0)=0=u(1), whereλ>0a parameter andf∈C(ℝ,ℝ)andf(0)>0andhmay change signs or may be beyond ofL1(0,1).