Abstract: Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established, where [φ(x)] =(|x |p-2x) with p > 1. Our result is new even when [φ(x)] = x in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.

Key words: solutions, second order p-Laplacian differential equation, two-point boundary
value problem, fixed-point theorem