Solvability of some boundary value problems involving p-Laplacian and non-autonomous differential operators

Abstract

The paper deals with the existence and non-existence of solutions of the following nonlinear non-autonomous boundary value problem governed by the p-Laplacian operator: (P) (h(t, x(t))|x (t)| p-2 x (t)) = g(t, x(t), x (t)) a.e. t ∈ R, x(-∞) = a, x(+∞) = b with a < b, where a is a positive, continuous function and g is a Caratheódory nonlinear function. We prove an existence result, underlying the relationship between the behavior of g(t, x, •) as y → 0 related to that of g(•, x, y) and h(•, x) as |t| → +∞.