Giuliana Palmieri

An existence result for nonlinear elliptic problems involving critical Sobolev exponent

Abstract In this paper we consider the following problem: (1) { − Δ u − λ u = | u | 2 ⁎ − 2 ⋅ u u = 0 on ∂ Ω 2 ⁎ = 2 n / ( n − 2 ) where Ω ⊂ Rn is a bounded domain and λ ∈ R. We prove the existence of a nontrivial solution of (1) for any λ > 0, if n ⩾ 4.

Radial solutions of semilinear elliptic equations with broken symmetry

The aim of this paper is to prove the existence of infinitely many radial solutions of a superlinear elliptic problem with rotational symmetry and non-homogeneous boundary data.

Multiple Solutions for p -Laplacian Type Problems with an Asymptotically p -linear Term

The aim of this paper is studying the asymptotically p-linear problem \( \left\{\begin{array}{clclcl}{\rm{-div}(A(x,u)|\bigtriangledown|_{u}|^{p-2}\bigtriangledown u)+ \frac{1}{p}A_{t}(x,u)|\bigtriangledown u|^{p}} \\ {\qquad = \; \lambda|u|^{p-2}u+g(x,u) \qquad \qquad \qquad \rm {in} \Omega} \\ {u=0 \qquad \qquad\qquad\qquad \qquad \qquad\qquad\qquad\rm{on}\; \partial \Omega},\end{array} \right.\) where \( \Omega \subset \mathbb{R}^{N} \) is an open bounded domain and \( p > N \geq 2 \). Suitable assumptions both at infinity and in the origin on the even function A(x, ·) and the odd map g(x, ·) allow us to prove the existence of multiple solutions by means of variational tools and the pseudo-index theory related to the genus in \( W^{1,p}_{0}(\Omega) \).

Multiple Solutions of Some Nonlinear Variational Problems

Abstract The aim of this paper is to prove some existence and multiplicity results for functionals of type J(u) = ∫Ω A(x, u)|▽u|2dx - ∫Ω G(x, u)dx, u 2 D ∊ H01 (Ω), with bounded domain Ω in ℝN. Since, in general, J is not Gâteaux differentiable in D, we study its restriction on the Banach space X = H01 (Ω) ∩ L∞(Ω) and apply some abstract existence and multiplicity theorems involving a variant of condition (C) below.

Multiplicity results for some quasilinear equationsin lack of symmetry

Abstract. In this paper we prove the existence of multiple nontrivial solutions for the quasilinear equation in divergence form, in an open bounded domain , where is a given Carathéodory function with partial derivatives and . It generalizes the -Laplacian problem but, in general, the corresponding functional is not well defined in all the space . Anyway, under suitable assumptions and by using variational tools, we are able to prove that the number of solutions for the above general problem depends on the parameter and, even in lack of symmetry, at least three nontrivial solutions exist if is large enough.