In this work we study the homogenization problem for (nonlinear) eigenvalues of quasilinear elliptic operators. We prove convergence of the first and second eigenvalues and, in the case where the operator is independent ...

In this paper, we use minimax methods, comparison arguments, and an approximation result to show the existence and multiplicity of solutions for the following class of problems: {-Δ1v=λf(v)inΩ,v≥0inΩ,v=0on∂Ω,where Ω is a ...

In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as ...

In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties ...

In this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One ...

Using variational methods we show the existence of a positive Multi-Bump solutions for the following class of quasilinear problems:    −∆pu + (λV (x) + Z(x))u p−1 = f(u), on R N u ∈ W1,p(R N ), (Pλ) where ∆pu ...

We present results of Ambrosseti-Prodi type to quasilinear problems involving the p-Laplace operator. We consider the scalar case and a a problem with systems of equations. In the scalar case, we work with the conditions ...