Lyapunov-type inequalities for third order nonlinear equations

Abstract

. We derive Lyapunov-type inequalities for general third order nonlinear equations in- volving multiple ψ -Laplacian operators of the form where ψ 2 and ψ 1 are odd, increasing functions, ψ 2 is super-multiplicative, ψ 1 is sub-multiplicative, and 1 ψ 1 is convex, and f is a continuous function which satisfies a sign condition. Our results utilize q + and q − , as opposed to | q | which appears in most results in the literature. Addi- tionally, these new inequalities generalize previously obtained results, and the proofs utilize a different technique than most other works in the literature. Furthermore, using the obtained in- equalities, we obtain a constraint on the location of the maximum of a solution, properties of oscillatory solutions, and an upper bound for the number of zeroes.