Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom ...Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.展开更多
文摘Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.
