Quasilinear elliptic Hamilton–Jacobi equations on complete manifolds

Quasilinear elliptic inequalities on complete Riemannian manifolds

We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some...

Nodal solutions to quasilinear elliptic equations on compact Riemannian manifolds

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.

On Quasilinear Elliptic Equations in Ir

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.

A Note on Quasilinear Parabolic Equations on Manifolds

We prove short time existence, uniqueness and continuous dependence on the initial data of smooth solutions of quasilinear locally parabolic equations of arbitrary even order on closed manifolds. CONTENTS

Large Solutions for Quasilinear Elliptic Equations