Author
Antonio Azzollini
Other affiliations: University of Bari
Bio: Antonio Azzollini is an academic researcher from University of Basilicata. The author has contributed to research in topics: Nonlinear system & Maxwell's equations. The author has an hindex of 21, co-authored 51 publications receiving 1518 citations. Previous affiliations of Antonio Azzollini include University of Bari.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the existence and nonexistence of ground state solutions for nonlinear Schrodinger-Maxwell equations were proved for 2 p 5 and 3 p 5, respectively, under the assumption that V is a positive constant.
366 citations
TL;DR: In this article, the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in R^3,$ assuming on the non-linearity the general hypotheses introduced by Berestycki & Lions was proved.
Abstract: In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions.
164 citations
TL;DR: In this article, the existence of a nontrivial solution to the non-linear Schrodinger-Maxwell equations in R 3, assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions, was proved.
Abstract: In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger–Maxwell equations in R 3 , assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.
139 citations
Journal Article•
TL;DR: In this paper, the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case was proved, and it was shown that such a solution can be obtained in the presence of a single generator.
Abstract: In this paper we prove the existence of a ground state solution for the nonlinear Klein–Gordon–Maxwell equations in the electrostatic case.
80 citations
TL;DR: In this article, the authors proved the existence of a positive solution to the problem Δu + V(x)u = g(u) in R N, assuming the general hypotheses on the nonlinearity introduced by Berestycki and Lions.
Abstract: In this paper we prove the existence of a positive solution to the equation -Δu + V(x)u = g(u) in R N , assuming the general hypotheses on the nonlinearity introduced by Berestycki and Lions. Moreover we show that a minimizing problem, related to the existence of a ground state, has no solution.
77 citations
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TL;DR: In this paper, a variational approach is proposed to solve a class of Schrodinger equations involving the fractional Laplacian, which is variational in nature and based on minimization on the Nehari manifold.
Abstract: We construct solutions to a class of Schrodinger equations involving the fractional Laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.
419 citations
TL;DR: In this paper, the existence and nonexistence of ground state solutions for nonlinear Schrodinger-Maxwell equations were proved for 2 p 5 and 3 p 5, respectively, under the assumption that V is a positive constant.
366 citations
TL;DR: A survey of the existence and properties of solutions to the Choquard type equations can be found in this paper, where some variants and extensions of its variants can also be found.
Abstract: We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations
$$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$
and some of its variants and extensions.
352 citations
TL;DR: In this article, the authors prove the existence of a nontrivial solution to the nonlinear Choquard equation in ℝ^N, where I_α is a Riesz potential.
Abstract: We prove the existence of a nontrivial solution 𝑢 ∈ H¹ (ℝ^N) to the nonlinear Choquard equation -Δ 𝑢 + 𝑢 = (I_α * 𝐹 (𝑢)) 𝐹' (𝑢) in ℝ^N, where I_α is a Riesz potential, under almost necessary conditions on the nonlinearity 𝐹 in the spirit of Berestycki and Lions. This solution is a groundstate; if moreover 𝐹 is even and monotone on (0, ∞), then 𝑢 is of constant sign and radially symmetric.
314 citations
TL;DR: In this article, the authors studied the nonlinear problem of Kirchhoff type with pure power nonlinearities and proved that (0.1) has a positive ground state solution by using a monotonicity trick and a new version of global compactness lemma.
310 citations