An Ill-posed estimate for a class of degenerate quasilinear elliptic equations

Existence of solutions for quasilinear degenerate elliptic equations ∗

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form A(u) + g(x, u,∇u) = h, where A is a Leray-Lions operator from W 1,p 0 (Ω, w) to its dual. On the nonlinear term g(x, s, ξ), we assume growth conditions on ξ, not on s, and a sign condition on s.

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Multi–peak Solutions for a Class of Degenerate Elliptic Equations

By means of a penalization argument due to del Pino and Felmer, we prove the existence of multi–spike solutions for a class of quasilinear elliptic equations under natural growth conditions. Compared with the semilinear case some difficulties arise, mainly concerning the properties of the limit equation. The study of concentration of the solutions requires a somewhat involved analysis in which ...

And Pointwise Estimates for a Class of Degenerate Elliptic Equations

In this paper we prove a Sobolev-Poincaré inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Holder regularity of the weak solutions follows in a standard way. 1 Let Sf = YJl ,=i 9j(ajjdj) be a second-order degenerate ellipt...

Existence Results for a Class of Semilinear Degenerate Elliptic Equations

We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.