Orlicz–Sobolev versus Hölder local minimizer and multiplicity results for quasilinear elliptic equations

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Regularity Results for Quasilinear Elliptic Equations in the Heisenberg Group

We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H. The model case is the nondegenerate p-Laplacean operator

Sturmian Comparison Results for Quasilinear Elliptic Equations in R

We obtain Sturmian comparison results for the nonnegative solutions to Dirichlet problems associated with p-Laplacian operators. From Picone-type identities [4, 9], we obtain results comparing solutions of two types of equations. We also present results related to those operators using Piconetype identities.

Multiplicity of solutions for quasilinear elliptic boundary-value problems

This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.

Large Solutions for Quasilinear Elliptic Equations