Topological Methods in Nonlinear Analysis

Multiple nonsemitrivial solutions for a class of degenerate quasilinear elliptic systems

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

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

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.