Uberlandio B. Severo

A result of multiplicity of solutions for a class of quasilinear equations

We establish the multiplicity of positive weak solutions for the quasilinear Dirichlet problem −L p u + | u | p−2 u = h(u) in Ω λ , u = 0 on ∂Ω λ , where Ω λ = λΩ, Ω is a bounded domain in ℝ N , λ is a positive parameter, L p u ≐ Δ p u + Δ p ( u 2 ) u and the nonlinear term h ( u ) has subcritical growth. We use minimax methods together with the Lyusternik–Schnirelmann category theory to get multiplicity of positive solutions.

On a class of nonhomogeneous elliptic problems involving exponential critical growth

In this paper we establish the existence of solutions for elliptic equations of the form

On a Class of Semilinear Elliptic Eigenvalue Problems in ℝ 2

-\text{div}(|\nabla u|^{n-2}\nabla u) + V(x)|u|^{n-2}u=g(x,u)+\lambda h

Stationary Schrödinger equations in with unbounded or vanishing potentials and involving concave nonlinearities

in

On a nonhomogeneous and singular quasilinear equation involving critical growth in R2

\mathbb{R}^n

On a quasilinear nonhomogeneous elliptic equation with critical growth in R N

with

Solitary waves for a class of quasilinear Schrödinger equations in dimension two

n\geq2

A nonhomogeneous elliptic problem involving critical growth in dimension two

. Here the potential

An improvement for the Trudinger–Moser inequality and applications

V(x)

Multiplicity of positive solutions for a class of quasilinear problems

can change sign and the nonlinearity