João R. Santos Júnior

Multiplicity Results for an Anisotropic Equation with Subcritical or Critical Growth

Abstract In this work we show some multiplicity results for the anisotropic equation where Ω ⊂ℝN is a bounded smooth domain, 1 < p1 ≤ p2 ≤ . . . ≤ pN and λ is a positive parameter. Using genus theory, we study the subcritical case gλ(u) = λ|u|q−2u with q ∈ (1, pN) and the critical case gλ(u) = λ|u|q−2u +|u|p*−2u with q ∈ (1, p1) and p* = N| p̅/(N−p̅), with p̅ the harmonic mean of the pi’s.

Existence and uniqueness of solution for a nonhomogeneous nonlocal problem

In this paper we analyze a class of elliptic problems involving a nonlocal Kirchhoff-type operator with variable coefficients and with a sign-changing datum. Under appropriated conditions on the coefficients, we have shown existence and uniqueness of solution.

On a generalized Kirchhoff equation with sublinear nonlinearities

In this paper, we consider a generalized Kirchhoff equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem, we show that, with a simple change of variable, the equation can be reduced to a classical semilinear equation and then studied with standard tools. Copyright