Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation

  • Bo Liang
  • Linghua Kong
  • Fuming Huang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 163)


The paper is devoted to studying a fourth order elliptic equation which has many applications in thin film theory and in the phase transformation theory. By using a truncation function method and a fixed point theorem, the existences of weak solutions and classic solutions for a steady state thin film equation are obtained respectively. Furthermore, the solutions also have positive lower bound. Finally, the viscosity vanishing limit is performed for positive solutions.


Fourth order Steady state Higher order 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of ScienceDalian Jiaotong UniversityDalianPeople’s Republic of China
  2. 2.School of ScienceDalian Ocean UniversityDalianPeople’s Republic of China

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