Let, (V, a(u, v)), (H, (u, v)) Hilbert spaces and the immersion V H is dense and compact. We consider the abstract problem: { Bu" + M(|u|)Au = f (*) Where B : H → H is a linear simetric and positive operator, (W, (W,|u|0), is a C1class Banach space, the non linear M is class and strictively positive. In this article we prove the existence and unicity of the local solution of the problem (*).
