Lyapunov Type Inequalities and Their Applications for Quasilinear Impulsive Systems

Abstract

A novel Lyapunov-type inequality for Dirichlet problem associated with the quasilinear impulsive system involving the (p(j), q(j))-Laplacian operator for j = 1,2 is obtained. Then utility of this new inequality is exemplified in finding disconjugacy criterion, obtaining lower bounds for associated eigenvalue problems and investigating boundedness and asymptotic behaviour of oscillatory solutions. The effectiveness of the obtained disconjugacy criterion is illustrated via an example. Our results not only improve the recent related results but also generalize them to the impulsive case.