A SHARP SUFFICIENT CONDITION FOR SOLUTION OF A NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEM,

Abstract

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 < g(x) = or < g(infinity) for all real x. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1969
Accession Number
AD0690556

Entities

People

  • S. C. Williams

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Equations
  • Mathematics
  • Numbers
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.