Abstract We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences critical points these satisfying the expected Morse index bounds as Lazer–Solimini’s theory, together with entropy condition Michael Struwe.

Su cient criteria are established for the existence of T -periodic solutions of a family of Lazer-Solimini equations with state-dependent delay. The method of proof relies on a combination of Leray-Schauder degree and a priori bounds.

A well-known theorem proved by A. C. Lazer and S. Solimini claims that the singular equation u′′ + 1 uλ = h(t), λ > 0, has a periodic solution if and only if the mean value of the continuous external force is positive. In this paper, we show that this result cannot be extended to the case when h is an integrable function, unless the additional assumptions are introduced. In addition, for each p...

Matthew Tan, Hiromi I. Wettersten, Kristy Chu, David L. Huso, Terry Watnick, Sharon Friedlander, Yosef Landesman, and Robert H. Weiss Graduate Group in Comparative Pathology, Division of Nephrology, Department of Internal Medicine, and Cancer Center, University of California, Davis, California; Department of Molecular and Comparative Pathobiology, Johns Hopkins University School of Medicine, Ba...

When the range of the derivative of the nonlinearity contains the rst k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in 5], where the existence of k + 1 solutions was proven.

Traveling Waves in a Suspension Bridge System by Robert A. Ain, Jr. Dr. Zhonghai Ding, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas In this thesis, we study the traveling waves in a Lazer-McKenna suspension bridge system which is governed by two coupled nonlinear beam and wave equations. The Lazer-McKenna suspension bridge system describes the v...