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Mathematics
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Advances in Nonlinear Analysis and Applications
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Advances in Nonlinear Analysis and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 3309

Special Issue Editor

Dr. Dhananjay Gopal

E-Mail Website
Guest Editor
1. Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, Chhattisgarh, India
2. Department of Mathematics, University of Jaén, 23071 Jaen, Spain
Interests: nonlinear analysis; fixed point theory; fuzzy mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear analysis plays a crucial role in addressing complex problems that arise across diverse fields such as physics, biology, computer science, mechanics, economics, and more.

This Special Issue focuses on the latest developments in nonlinear analysis and its wide-ranging applications. Nonlinear analysis, which is part of the broader field of nonlinear functional analysis, has seen significant growth in recent years due to its relevance to a variety of scientific and engineering challenges.

We invite contributions that explore both the theoretical advancements and practical applications of nonlinear analysis. This includes, but is not limited to, topics such as:

  • Nonlinear ergodic theory and its applications
  • Solutions to differential equations and control theory
  • Dynamical systems and bifurcation theory
  • Mathematical modeling of nonlinear phenomena
  • Optimization, equilibrium, and split feasibility problems
  • Applications of fixed-point theory to nonlinear issues
  • Convergence and stability of iterative algorithms

We are particularly interested in high-quality articles that offer new concepts, methodologies, algorithms, and demonstrate practical applications in various scientific disciplines.

Dr. Dhananjay Gopal
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear analysis
  • nonlinear functional analysis
  • nonlinear differential equations
  • dynamical systems
  • bifurcation theory
  • nonlinear ergodic theory
  • variational inequalities
  • fixed-point theory
  • nonlinear phenomena

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

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18 pages, 326 KB  
Article
Existence of Solutions to the Nonstationary Stokes System with a Nonlinear Overdetermination Condition
by Vytautas Bačianskas and Kristina Kaulakytė
Mathematics 2026, 14(9), 1402; https://doi.org/10.3390/math14091402 - 22 Apr 2026
Viewed by 287
Abstract
In this paper, we study an inverse problem for the nonstationary Stokes system in a bounded domain Ω with a nonlinear integral overdetermination condition, describing the kinetic energy E(t) of the fluid. We construct two classes of solutions: weak and [...] Read more.
In this paper, we study an inverse problem for the nonstationary Stokes system in a bounded domain Ω with a nonlinear integral overdetermination condition, describing the kinetic energy E(t) of the fluid. We construct two classes of solutions: weak and very weak. In the case where the kinetic energy E belongs to W21(0,T), we construct weak solutions. If E belongs only to L2(0,T), we construct very weak solutions. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
23 pages, 339 KB  
Article
Composite Lyapunov Criteria for Stability and Convergence with Applications to Optimization Dynamics
by Hassan Saoud
Mathematics 2025, 13(23), 3859; https://doi.org/10.3390/math13233859 - 2 Dec 2025
Viewed by 618
Abstract
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of dissipation measures, convergence to a critical set, and semistability under mild conditions, without [...] Read more.
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of dissipation measures, convergence to a critical set, and semistability under mild conditions, without relying on invariance principles or compactness assumptions. The framework unifies convergence to points and sets and is illustrated through applications to inertial gradient systems and Primal–Dual gradient flows. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
15 pages, 469 KB  
Article
Observer-Based Local Stabilization of State-Delayed Quasi-One-Sided Lipschitz Systems with Actuator Saturation
by Ali Aloui, Omar Kahouli, Mohamed Ayari, Hamdi Gassara and Lilia El Amraoui
Mathematics 2025, 13(22), 3610; https://doi.org/10.3390/math13223610 - 11 Nov 2025
Viewed by 564
Abstract
This paper addresses the problem of asymptotic stabilization for a class of systems composed of linear and nonlinear parts, both of which are affected by a common state delay that increases the complexity of the dynamics. Within this class of systems, the nonlinear [...] Read more.
This paper addresses the problem of asymptotic stabilization for a class of systems composed of linear and nonlinear parts, both of which are affected by a common state delay that increases the complexity of the dynamics. Within this class of systems, the nonlinear component depends on unmeasurable states and satisfies a quasi-one-sided Lipschitz (QL) condition, which allows for tractable analysis. Moreover, the control input is subject to saturation, further complicating the stabilization task. The proposed remedy involves three key components: an observer to estimate the unmeasurable states, a Lyapunov–Krasovskii (LK) functional to handle the delay, and a dead-zone model to represent the saturation nonlinearity. This combined approach allows for the derivation of sufficient conditions that ensure the local asymptotic stabilization of an augmented system comprising the state and the estimation error. Furthermore, the domain of attraction is estimated. The obtained conditions are not LMIs. This arises from a shared matrix variable that is required to simultaneously verify the weak QL Lipschitz condition and appear within the LK functional, creating a nonlinear coupling. In the existing literature, this matrix is typically fixed and not treated as a decision variable to simplify the problem. In contrast, this work proposes a novel approach by employing an appropriate decoupling technique, which allows this matrix to remain a decision variable and provides greater flexibility in the design. To validate the proposed design, we provide a numerical simulation. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
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Review

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35 pages, 474 KB  
Review
Developments in Modular Space Fixed Point Theory
by Wojciech M. Kozlowski
Mathematics 2026, 14(7), 1234; https://doi.org/10.3390/math14071234 - 7 Apr 2026
Viewed by 492
Abstract
This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the [...] Read more.
This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the modular sense, and the results can also be applied directly to Banach spaces. Utilizing the framework of regular and super-regular modular spaces, our research generalizes several established results concerning fixed points of nonlinear operators, applicable to both Banach spaces and modular function spaces. The study seeks to identify and discuss current challenges, knowledge gaps, and unresolved questions, providing insights into the potential of future research opportunities. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
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