Topological Methods in Nonlinear Analysis

On the existence of positive entire solutions of nonlinear elliptic equations

Marco Squassina

Full-text: Open access

Abstract

Via non-smooth critical point theory, we prove existence of entire positive solutions for a class of nonlinear elliptic problems with asymptotic $p$-Laplacian behaviour and subjected to natural growth conditions.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 17, Number 1 (2001), 23-39.

Dates
First available in Project Euclid: 22 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1471875795

Mathematical Reviews number (MathSciNet)
MR1846976

Zentralblatt MATH identifier
0997.35019

Citation

Squassina, Marco. On the existence of positive entire solutions of nonlinear elliptic equations. Topol. Methods Nonlinear Anal. 17 (2001), no. 1, 23--39. https://projecteuclid.org/euclid.tmna/1471875795


Export citation

References

  • D. Arcoya and L. Boccardo, Critical points for multiple integrals of the calculus of variations , Arch. Rational Mech. Anal., 134(1996), 249–274 \ref\key 2
  • M. Badiale and G. Citti, Concentration compactness principle and quasilinear elliptic equations in $\R^n$ , Comm. Partial Differential Equations, 16(1991), 1795–1818 \ref\key 3
  • V. Benci and G. Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains , Arch. Rational Mech. Anal., 99(1987), 283–300 \ref\key 4
  • H. Berestycki and P. L. Lions, Nonlinear scalar field equation I, existence of a ground state , Arch. Rational Mech. Anal., 82(1983), 313–346 \ref\key 5
  • L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations , Nonlinear Anal., 19(1992), 581–597 \ref\key 6
  • D. Cao and X. Zhu, The concentration-compactness principle in nonlinear elliptic equations , Acta Math. Sci., 9(1989), 307–328 \ref\key 7
  • A. Canino and M. Degiovanni, Nonsmooth critical point theory and quasilinear elliptic equations , Topological Methods in Differential Equations and Inclusions, 1–50 (A. Granas, M. Frigon, G. Sabidussi, eds.), Montreal (1994);, NATO Adv. Sci. Inst. Ser. (1995) \ref\key 8
  • G. Citti, Existence of positive solutions of quasilinear degenerate elliptic equations on unbounded domains , Ann. Mat. Pura Appl. (4), 158(1991), 315–330 \ref\key 9
  • M. Conti and F. Gazzola, Positive entire solutions of quasilinear elliptic problems via nonsmooth critical point theory , Topol. Methods Nonlinear Anal., 8(1996), 275–294 \ref\key 10
  • J. N. Corvellec, M. Degiovanni and M. Marzocchi, Deformation properties for continuous functionals and critical point theory , Topol. Methods Nonlinear Anal., 1(1993), 151–171 \ref\key 11
  • M. Degiovanni and M. Marzocchi, A critical point theory for nonsmooth functionals , Ann. Mat. Pura Appl. (4), 167(1994), 73–100 \ref\key 12