Solvability of the Φ-Laplacian with nonlocal boundary conditions

Rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form[Φ(x′(t))]′+c(t)(Fx)(t)=0,a.a.t∈(0,1),x(0)-L0(x)=x(1)-L1(x)=0,which unify several cases discussed in the literature. In order to formulate these conditions one needs to know only properties of the homeomorphism Φ:R→R and have information about the level of growth of the response operator F. No metric information concerning the linear operators L0,L1 in the boundary conditions is used, except that they are positive and continuous and such that Lj(1)<1 j∈{0,1}.