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Positive solutions of semilinear elliptic boundary value problems

  • Klaus Schmitt
Chapter
Part of the NATO ASI Series book series (ASIC, volume 472)

Abstract

The paper is concerned with existence questions for positive solutions (ground states) of boundary value problems for semilinear elliptic partial differential equations. Global continuation and bifurcation results are used to obtain the existence of unbounded solution continua whenever the nonlinear terms depend upon a real parameter. Results are presented for various classes of nonlinear terms which are classified depending on their asymptotic growth, such as linear, superlinear, subcritical, and supercritical growth. Results describing the influence of the geometry, topology and dimension of the domain on the solution structure are also discussed.

Keywords

Solution Continuum Nonlinear Elliptic Equation Radial Solution Principal Eigenvalue Critical Sobolev Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Klaus Schmitt
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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