Multiple nonsemitrivial solutions for a class of degenerate quasilinear elliptic systems. (English) Zbl 1375.35209

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

Topol. Methods Nonlinear Anal. 45, No. 2, 385-397 (2015).

The existence of multiple nonsemitrivial solutions for a degenerate quasilinear system depending on a parameter \(\lambda\) is proved. The variational approach is applied, based on the notion of Nehari manifolds, and a result for an eigenvalue problem proved by the third author. The main result is Theorem 3.5 on the existence of nonnegative nonsemitrivial solutions for \(\lambda\) in an specified interval. The proof is technical and original.

Reviewer: Stepan Agop Tersian (Rousse)

MSC:

35J62	Quasilinear elliptic equations
35J50	Variational methods for elliptic systems

Keywords:

quasilinear systems; Nehari manifolds; variational methods