Asymptotic Analysis - Volume 105, issue 3-4

Authors: Morse, Matthew R. | Spiliopoulos, Konstantinos

Article Type: Research Article

Abstract: In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and the homogenization regimes. We allow the coefficients to be in the whole space and not just the torus and allow the noises driving the slow and fast processes to be correlated arbitrarily. Similar to the large deviation case, the methodology that we follow allows construction of provably efficient Monte Carlo methods for rare events that fall into the moderate deviations regime.

Keywords: Moderate deviations, slow-fast diffusions, multiscale processes, stochastic control, Laplace principle

DOI: 10.3233/ASY-171434

Citation: Asymptotic Analysis, vol. 105, no. 3-4, pp. 97-135, 2017

Authors: Heidarkhani, Shapour | Afrouzi, Ghasem A. | Moradi, Shahin

Article Type: Research Article

Abstract: We shall discuss the existence of at least one weak solution and infinitely many weak solutions for a Kirchhoff-type second-order impulsive differential equation on the half-line. Our technical approach is based on variational methods. Some recent results are extended and improved. Some examples are presented to demonstrate the application of our main results.

Keywords: Half-line, impulsive differential equation, Kirchhoff-type problem, one weak solution, infinitely many weak solutions, variational methods

DOI: 10.3233/ASY-171437

Citation: Asymptotic Analysis, vol. 105, no. 3-4, pp. 137-158, 2017

Authors: Ambrosio, Vincenzo | Figueiredo, Giovany M.

Article Type: Research Article

Abstract: In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation ( − Δ ) s u + V ( x ) u = f ( u ) in  R N , where s ∈ ( 0 , 1 ) , N > 2 s , ( − Δ ) s is the fractional Laplacian, V : R N → R …is a bounded potential satisfying suitable assumptions, and f ∈ C 1 , β ( R , R ) has critical growth. We first analyze the case V constant, and then we develop a Jeanjean–Tanaka argument [Indiana Univ. Math. J. 54 (2005), 443–464] to deal with the non autonomous case. As far as we know, all results presented here are new. Show more

Keywords: Fractional Laplacian, monotonicity trick, critical exponent, compactness lemma

DOI: 10.3233/ASY-171438

Citation: Asymptotic Analysis, vol. 105, no. 3-4, pp. 159-191, 2017