Topological Methods in Nonlinear Analysis

On the existence of positive entire solutions of nonlinear elliptic equations

Marco Squassina

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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.

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

First available in Project Euclid: 22 August 2016

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Squassina, Marco. On the existence of positive entire solutions of nonlinear elliptic equations. Topol. Methods Nonlinear Anal. 17 (2001), no. 1, 23--39.

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  • 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