A semilinear wave equation with nonmonotone nonlinearity

Alfonso Castro and Sumalee Unsurangsie

Vol. 132 (1988), No. 2, 215–225

DOI: 10.2140/pjm.1988.132.215

Abstract

We prove that a semilinear wave equation in which the range of the derivative of the nonlinearity includes an eigenvalue of infinite multiplicity has a solution. The solution is obtained through an iteration scheme which provides a priori estimates.

Mathematical Subject Classification 2000

Primary: 35L70

Secondary: 35L20

Milestones

Received: 15 December 1986

Published: 1 April 1988