On Lyapunov-type inequalities for ( p , q ) $(p,q)$ -Laplacian systems

LYAPUNOV–TYPE INEQUALITIES FOR HIGHER–ORDER DIFFERENTIAL EQUATIONS WITH ONE–DIMENSIONAL p–LAPLACIAN

In this paper, we establish Lyapunov-type inequalities for a single higher-order differential equation, a cycled system and a coupled system with one-dimensional p -Laplacian. Our result generalize some given results.

Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

On Lyapunov-type inequalities for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}(p,q)-Laplacian systems

*Correspondence: [email protected] Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia Abstract We establish Lyapunov-type inequalities for a system involving one-dimensional (pi ,qi)-Laplacian operators (i = 1, 2). Next, the obtained inequalities are used to derive some geometric properties of the generalized spectrum associated to th...

Existence of weak solutions for a class of (p,q)$(p,q)$-Laplacian systems

Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems

In this paper, we establish several new Lyapunov-type inequalities for the first-order nonlinear Hamiltonian system  x ′ (t) = α(t)x(t) + β(t)|y(t)| µ−2 y(t), y ′ (t) = −γ (t)|x(t)| ν−2 x(t) − α(t)y(t), which generalize or improve all related existing ones.