Existence of solutions to integral type BVPs for second order ODEs on the whole line

Some integral type boundary value problems (BVPs) for second order differential equations (ODEs) with one-dimensional p-Laplacian on the whole line are discussed. Sufficient conditions to guarantee the existence of solutions are established. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x'(t))]' involved with the nonnegative function ρ that may satisfy $\rho(0)=0$, and the differential equations are defined on the whole line.