Roberta Filippucci

Existence and Non-Existence Results for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions

Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition between the different growths of the nonlinearities.

NONLINEAR WEIGHTED p-LAPLACIAN ELLIPTIC INEQUALITIES WITH GRADIENT TERMS

In this paper, we give sufficient conditions for the existence and nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p-2Du} ≥ h(|x|)f(u)l(|Du|). We achieve our conclusions by using a generalized version of the well-known Keller–Ossermann condition, first introduced in [2] for the generalized mean curvature case, and in [11, Sec. 4] for the nonweighted p-Laplacian equation. Several existence results are also proved in Secs. 2 and 3, from which we deduce simple criteria of independent interest stated in the Introduction.

Coercive elliptic systems with gradient terms

Abstract In this paper we give a classification of positive radial solutions of the following system: Δ ⁢ u = v m , Δ ⁢ v = h ⁢ ( | x | ) ⁢ g ⁢ ( u ) ⁢ f ⁢ ( | ∇ ⁡ u | ) ,

On a p-Laplace equation with multiple critical nonlinearities

\Delta u=v^{m},\quad\Delta v=h(|x|)g(u)f(|\nabla u|),

Nonexistence of positive weak solutions of elliptic inequalities

in the open ball B R

Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights

{B_{R}}

EXISTENCE OF RADIAL SOLUTIONS FOR THE P{LAPLACIAN ELLIPTIC EQUATIONS WITH WEIGHTS

, with m > 0

On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms

{m>0}

On weak solutions of nonlinear weighted p{Laplacian elliptic inequalities

, and f, g, h nonnegative nondecreasing continuous functions. In particular, we deal with both explosive and bounded solutions. Our results involve, as in [27], a generalization of the well-known Keller–Osserman condition, namely, ∫ 1 ∞ ( ∫ 0 s F ⁢ ( t ) ⁢ 𝑑 t ) - m / ( 2 ⁢ m + 1 ) ⁢ 𝑑 s < ∞

Non-existence of nodal and one-signed solutions for nonlinear variational equations

{\int_{1}^{\infty}(\int_{0}^{s}F(t)\,dt)^{-m/(2m+1)}\,ds<\infty}