Localized solutions of elliptic equations: loitering at the hilltop.
Lower Norm Estimates for Approximate Solutions of Differential Equations with Non-Smooth Coefficients.
Lp-Perturbations of Second Order Linear Differential Equations.
Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues
Lyapunov inequalities for one-dimensional -Laplacian problems with a singular weight function.
Lyapunov type inequalities for a second order differential equation with a damping term
For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type...