MULTIPLE SOLUTIONS FOR INHOMOGENEOUS ELLIPTIC PROBLEMS ARISING IN ASTROPHYSICS

By variational and topological methods we prove the existence of a positive interval LAMBDA such that for all lambda is-an-element-of LAMBDA there exist at least three positive solutions of (1.1) on OMEGA = D(R), where D(R) is a semidisk in R+2 with radius R and center (0, 0), h is a non-negative bounded smooth function and f : R --> R is a function of type (t(sigma) - t(sigma+alpha))chi[0,1](t) with sigma > 1 and alpha > 0. Under some restrictions for f and h we show that LAMBDA is independent of R, for R large enough. This type of problem arises in an astrophysical gravity-free model of solar flares given by J. Heyvaerts and others.