Topological Methods in Nonlinear Analysis

Multiple nonsemitrivial solutions for a class of degenerate quasilinear elliptic systems

Ghasem A. Afrouzi, Armin Hadjian, and Nicolaos B. Zographopoulos

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove the existence of multiple nonnegative nonsemitrivial solutions for a degenerate quasilinear elliptic system. Our technical approach is based on variational methods.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 45, Number 2 (2015), 385-397.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1459343988

Digital Object Identifier
doi:10.12775/TMNA.2015.019

Mathematical Reviews number (MathSciNet)
MR3408828

Zentralblatt MATH identifier
1375.35209

Citation

Afrouzi, Ghasem A.; Hadjian, Armin; Zographopoulos, Nicolaos B. Multiple nonsemitrivial solutions for a class of degenerate quasilinear elliptic systems. Topol. Methods Nonlinear Anal. 45 (2015), no. 2, 385--397. doi:10.12775/TMNA.2015.019. https://projecteuclid.org/euclid.tmna/1459343988


Export citation

References

  • L. Boccardo and D.G. de Figueiredo, Some remarks on a system of quasilinear elliptic equations, NoDEA Nonlinear Differential Equations Appl. 9 (2002), 309–323.
  • G. Bonanno, S. Heidarkhani and D. O'Regan, Multiple solutions for a class of dirichlet quasilinear elliptic systems driven by a $(P,Q)$-Laplacian operator, Dynam. Systems Appl. 20 (2011), 89–100.
  • Y. Bozhkova and E. Mitidieri, Existence of multiple solutions for quasilinear systems via Fibering method, J. Differential Equations 190 (2003), 239–267.
  • R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. I: Physical Origins and Classical Methods, Springer–Verlag, Berlin, 1985.
  • A. Djellit and A. Tas, Existence of solutions for a class of elliptic systems in $\mathbb{R}^N$ involving the $p$-Laplacian, Electron. J. Differential Equations 56 (2003), 1–8.
  • P. Drábek and Y.X. Huang, Multiple positive solutions of quasilinear elliptic equations in $\mathbb{R}^N$, Nonlinear Anal. 37 (1999), 457-466.
  • P. Drábek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter & Co., Berlin, 1997.
  • P. Drábek, N.M. Stavrakakis and N.B. Zographopoulos, Multiple nonsemitrivial solutions for quasilinear elliptic systems, Differential Integral Equations 16 (2003), 1519–1531.
  • A. Kristály, Existence of two non-trivial solutions for a class of quasilinear elliptic variational systems on strip-like domains, Proc. Edinb. Math. Soc. (2) 48 (2005), 465–477.
  • Z.-Q. Ou and C.-L. Tang, Existence and multiplicity of nontrivial solutions for quasilinear elliptic systems, J. Math. Anal. Appl. 383 (2011), 423–438.
  • M.N. Poulou, N.M. Stavrakakis and N.B. Zographopoulos, Global bifurcation results on degenerate quasilinear elliptic systems, Nonlinear Anal. 66 (2007), 214–227.
  • N.M. Stavrakakis and N.B. Zographopoulos, Existence results for some quasilinear elliptic systems in $\mathbb{R}^N$, Electron. J. Differential Equations 39 (1999), 1–15.
  • N.B. Zographopoulos, On the principal eigenvalue of degenerate quasilinear elliptic systems, Math. Nachr. 281 (9) (2008), 1351–1365.