Asymptotic analysis of oscillating parametric integrals and ordinary boundary value problems at resonance ✩

This paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one-dimensional solution space. We shall study the existence and multiplicity of solutions using various methods of Nonlinear Analysis such as the Lyapunov–Schmidt reduction and methods of critical point theory. The proofs are based on some general results on the oscillation and asymptotic behavior of certain parametric integrals.  2005 Elsevier Inc. All rights reserved