New solutions of the Gelfand problem

Abstract

We propose a computer-assisted method for proving existence and obtaining enclosures of solutions of nonlinear elliptic boundary value problems, which may be successful in cases where purely analytic methods are not. This method is an extension of our previous work (Interval Comput. 3 (1994) 106–121, Z. Angew. Math. Mech. 76 (1996) 171–176) on the Gelfand problem to nonconvex domains in R2; here we are able to prove the existence of a solution branch which was unknown so far.