EXISTENCE OF TWO NON-TRIVIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC VARIATIONAL SYSTEMS ON STRIP-LIKE DOMAINS
EXISTENCE OF TWO NON-TRIVIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC VARIATIONAL SYSTEMS ON STRIP-LIKE DOMAINS
Abstract In this paper we study the multiplicity of solutions of the quasilinear elliptic system \begin{equation} \left. \begin{aligned} -\Delta_pu\amp=\lambda F_u(x,u,v)\amp\amp\text{in }\varOmega, \\ -\Delta_qv\amp=\lambda F_v(x,u,v)\amp\amp\text{in }\varOmega, \\ u=v\amp=0\amp\amp\text{on }\partial\varOmega, \end{aligned} \right\} \end{equation} \tag{S$_\lambda$} where $\varOmega$ is a strip-like domain and $\lambda>0$ is a parameter. Under some growth conditions on $F$, we …