A Sharp Sufficient Condition for Solution of a Nonlinear Elliptic Boundary Value Problem

摘要

The paper establishes a sufficient condition such that the equation Au + g(u) = h has a weak solution u with generalized Dirichlet data zero where A is any self-adjoint strongly and uniformly elliptic linear partial differential operator with real-valued, reasonably smooth coefficients defined on a bounded open set Omega of E superscript n, where h is square-integrable and real-valued on Omega, and where g is any continuous real-valued function defined for all real numbers such that g(infinity) = lim as x approaches infinity g(x) and g(minus infinity) = lim as x approaches minus infinity g(x) exist (and are finite) such that g(minus infinity) = or