Journal•ISSN: 1468-1218
Nonlinear Analysis-real World Applications
Elsevier BV
About: Nonlinear Analysis-real World Applications is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Nonlinear system & Uniqueness. It has an ISSN identifier of 1468-1218. Over the lifetime, 3420 publications have been published receiving 75541 citations.
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TL;DR: In this paper, the nonlocal Cauchy problem is discussed for the fractional evolution equations in an arbitrary Banach space and various criteria on the existence and uniqueness of mild solutions are obtained.
Abstract: In this paper, the nonlocal Cauchy problem is discussed for the fractional evolution equations in an arbitrary Banach space and various criteria on the existence and uniqueness of mild solutions are obtained. An example to illustrate the applications of main results is also given.
443 citations
TL;DR: In this paper, a new approach via variational methods and critical point theory is presented to obtain the existence of solutions to impulsive problems. But this approach is restricted to a linear Dirichlet problem and the solutions are found as critical points of a functional.
Abstract: Many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this work we present a new approach via variational methods and critical point theory to obtain the existence of solutions to impulsive problems. We consider a linear Dirichlet problem and the solutions are found as critical points of a functional. We also study the nonlinear Dirichlet impulsive problem.
396 citations
TL;DR: In this article, the global dynamics of SIR models with distributed delay and with discrete delay were studied and the endemic equilibrium was shown to be globally asymptotically stable whenever it exists.
Abstract: SIR models with distributed delay and with discrete delay are studied. The global dynamics are fully determined for R 0 > 1 by using a Lyapunov functional. For each model it is shown that the endemic equilibrium is globally asymptotically stable whenever it exists.
372 citations
TL;DR: In this article, the existence and uniqueness of mild solutions for semilinear fractional evolution equations and optimal controls in the α -norm were proved by means of fractional calculus, singular version Gronwall inequality and Leray-Schauder fixed point theorem.
Abstract: This paper concerns the existence of mild solutions for semilinear fractional evolution equations and optimal controls in the α -norm. A suitable α -mild solution of the semilinear fractional evolution equations is introduced. The existence and uniqueness of α -mild solutions are proved by means of fractional calculus, singular version Gronwall inequality and Leray–Schauder fixed point theorem. The existence of optimal pairs of system governed by fractional evolution equations is also presented. Finally, an example is given for demonstration.
358 citations
TL;DR: In this article, the following Schrodinger-Kirchhoff-type problem (1.1) − (a + b ∫ R N | ∇ u | 2 d x ) Δ u + V (x ) u = f ( x, u ), in R N is studied and four new existence results for nontrivial solutions and a sequence of high energy solutions for problem 1.1 are obtained by using a symmetric Mountain Pass Theorem.
Abstract: In the present paper, the following Schrodinger–Kirchhoff-type problem: (1.1) − ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( x , u ) , in R N is studied and four new existence results for nontrivial solutions and a sequence of high energy solutions for problem (1.1) are obtained by using a symmetric Mountain Pass Theorem.
278 citations