Topological Methods in Nonlinear Analysis

Solutions to some singular nonlinear boundary value problems

Beata Medak, Alexey A. Tret'yakov, and Henryk Żołądek

Full-text: Open access

Abstract

We apply the so-called $p$-regularity theory to prove the existence of solutions to two nonlinear boundary value problems: an equation of rod bending and some nonlinear Laplace equation.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 41, Number 2 (2013), 255-265.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461245477

Mathematical Reviews number (MathSciNet)
MR3114307

Zentralblatt MATH identifier
1293.35324

Citation

Medak, Beata; Tret'yakov, Alexey A.; Żołądek, Henryk. Solutions to some singular nonlinear boundary value problems. Topol. Methods Nonlinear Anal. 41 (2013), no. 2, 255--265. https://projecteuclid.org/euclid.tmna/1461245477


Export citation

References

  • M. Buchner, J. Marsden and S. Schechter, Applications of the blowing-up construction and algebraic geometry to bifurcation problems , J. Differential Equations, 48 (1983), 404–433 \ref\key 2
  • O.A. Brezhneva, A.A. Tret'yakov and J.E. Marsden, Higher order implicit function theorems and degenerate nonlinear boundary value problems , Comm. Pure Appl. Anal., 7 (2008), 293–315 \ref\key 3
  • A.F. Izmailov and A.A. Tret'yakov, Factor Analysis of Nonlinear Mappings, Nauka, Moscow (1994), (in Russian) \ref\key 4 ––––, 2-Regular Solutions of Nonlinear Problems. Theory and Numerical Methods, Nauka, Moscow (1999), (in Russian) \ref\key 5
  • J.E. Marsden and A.A. Tret'yakov, Factor analysis of nonlinear mappings: p-regularity theory , Comm. Pure Appl. Anal., 2 (2003), 425–445 \ref\key 6
  • V.A. Trenogin, Functional Analysis, Nauka, Moscow (1980), (in Russian) \ref\key 7
  • A.A. Tret'yakov, The implicit function theorem in degenerate problems , Russian Math. Surveys, 42 (1987), 179–180