Paper Title:

Nonlinear Elliptic Problems

Author(s):

Alexander G. Ramm

Department of Mathematics,
Kansas State University,
Manhattan, KS 66506-2602,
USA.
E-mail: ramm@ksu.edu

Abstract:

Let h(u)>0 be a smooth monotonically growing function, lim_u->∞h(u)|u|^^-1=+∞, f(x)≥ 0 is bounded. Consider a nonlinear elliptic problem -Δ u=h(u)+f in D⊂ R³, D is a bounded domain with a smooth boundary S, u=0 on S. We prove the existence of a solution to this problem.

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