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The existence and qualitative properties of nontrivial solutions for some important nonlinear Schrӧdinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground state solutions, including the existence, the nonexistence, the uniqueness and the phase separation phenomena of the limit profile has been presented, which seems to be the first contribution for BEC in the critical case. Furthermore, some quite different phenomena were also studied in a more general critical system. For the classical Brezis-Nirenberg critical exponent problem, the sharp energy estimate of least energy solutions in a ball has been investigated in this study. Finally, for Ambrosetti type linearly coupled Schrӧdinger equations with critical exponent, an optimal result on the existence and nonexistence of ground state solutions for different coupling constants was also obtained in this thesis. These results have many applications in Physics and PDEs.

Mathematics. --- Partial Differential Equations. --- Mathematical Applications in the Physical Sciences. --- Mathematical Physics. --- Differential equations, partial. --- Mathématiques --- Bose-Einstein condensation. --- Nonlinear optics. --- Nonlinear systems -- Mathematical models. --- System theory -- Mathematical models. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Nonlinear systems --- Mathematical models. --- Systems, Nonlinear --- Partial differential equations. --- Mathematical physics. --- System theory --- Partial differential equations --- Physical mathematics --- Physics

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Control of Complex Systems: Structural Constraints and Uncertainty focuses on control design under information structure constraints, with a particular emphasis on large-scale systems. The complexity of such systems poses serious computational challenges and severely restricts the types of feedback laws that can be used in practice. This book systematically addresses the main issues, and provides a number of applications that illustrate potential design methods, most which use Linear Matrix Inequalities (LMIs), which have become a popular design tool over the past two decades. Authors Aleksandar I. Zecevic and Dragoslav D. Siljak use their years of experience in the control field to also: Address the issues of large-scale systems as they relate to robust control and linear matrix inequalities Discuss a new approach to applying standard LMI techniques to large-scale systems, combining graphic-theoretic decomposition techniques with appropriate low-rank numerical approximations and dramatically reducing the computational effort Providing numerous examples and a wide variety of applications, ranging from electric power systems and nonlinear circuits to mechanical problems and dynamic Boolean networks Control of Complex Systems: Structural Constraints and Uncertainty will appeal to practicing engineers, researchers and students working in control design and other related areas. .

Computational complexity. --- Control theory. --- Mathematical optimization. --- System analysis -- Mathematical models. --- System analysis. --- System theory -- Mathematical models. --- Control theory --- Large scale systems --- Operations Research --- Mechanical Engineering - General --- Civil & Environmental Engineering --- Mechanical Engineering --- Engineering & Applied Sciences --- Complexity, Computational --- Mathematics. --- System theory. --- Vibration. --- Dynamical systems. --- Dynamics. --- Control engineering. --- Robotics. --- Mechatronics. --- Systems Theory, Control. --- Control. --- Control, Robotics, Mechatronics. --- Vibration, Dynamical Systems, Control. --- Electronic data processing --- Machine theory --- Dynamics --- Systems theory. --- Control and Systems Theory. --- Cycles --- Mechanics --- Sound --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Philosophy

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Modeling Complex Systems, 2nd Edition, explores the process of modeling complex systems, providing examples from such diverse fields as ecology, epidemiology, sociology, seismology, and economics. It illustrates how models of complex systems are built and provides indispensable mathematical tools for studying their dynamics. This vital introductory text is useful for advanced undergraduate students in various scientific disciplines, and serves as an important reference book for graduate students and young researchers. This enhanced second edition includes: . -recent research results and bibliographic references -extra footnotes which provide biographical information on cited scientists who have made significant contributions to the field -new and improved worked-out examples to aid a student’s comprehension of the content -exercises to challenge the reader and complement the material Nino Boccara is also the author of Essentials of Mathematica: With Applications to Mathematics and Physics (Springer, 2007).

Electronic books. -- local. --- System analysis -- Mathematical models. --- System theory -- Mathematical models. --- System theory --- System analysis --- Civil & Environmental Engineering --- Physics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Atomic Physics --- Mathematical models --- Mathematical models. --- Systems, Theory of --- Systems science --- Computer science. --- Algorithms. --- Computer simulation. --- Computer mathematics. --- Physics. --- Statistical physics. --- Dynamical systems. --- Computer Science. --- Simulation and Modeling. --- Algorithm Analysis and Problem Complexity. --- Computational Mathematics and Numerical Analysis. --- Statistical Physics, Dynamical Systems and Complexity. --- Numerical and Computational Physics. --- Computational Science and Engineering. --- Science --- Philosophy --- Computer software. --- Computer science --- Complex Systems. --- Numerical and Computational Physics, Simulation. --- Mathematics. --- Informatics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Software, Computer --- Computer systems --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Simulation methods --- Model-integrated computing --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mathematical statistics --- Algorism --- Algebra --- Arithmetic --- Statistical methods --- Foundations