Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems

Abstract

In this paper, we establish some new Lyapunov-type inequalities for a class of Laplacian systems. With these, sufficient conditions for the non-existence of nontrivial solutions to certain boundary value problems are obtained. A lower bound for the eigenvalues is also deduced.

Lyapunov type inequalities and their applications for quasilinear impulsive systems

“…The half linear version of Lyapunov inequality was obtained in [5][6][7][8][9]. To the best of our knowledge, although many results have been obtained for quasilinear systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23], there is little known for the impulsive quasilinear systems [24]. Although there is a large body of literature on quasilinear systems that we can not cover completely, the results in [10,11,24] and in [22] are worth mentioning due to their contribution to these subject.…”