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9780128036525 English 0128036524 Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditionsDiscusses second order difference equations with multi-point boundary conditionsIntroduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions, In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of maths as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions, The book contains the study of the existence, multiplicity, and nonexistence of positive solutions of several classes of boundary value problems for nonlinear systems of ordinary differential equations, difference equations, and fractional equations. The first two chapters are devoted to systems of nonlinear second-order or higher-order ordinary differential equations with Riemann-Stieltjes boundary conditions. Systems of nonlinear second-order difference equations subject to multi point boundary conditions are investigated in the third chapter. The last two chapters cover systems of nonlinear Riemann-Liouville fractional differential equations with either uncoupled or coupled integral boundary conditions. Various classes of systems - namely, systems with parameters or without parameters, systems with nonsingular or singular nonlinearities, and systems with sign-changing nonlinearities û are studied. In each chapter, various examples are presented which support the main results. Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions provides a comprehensive description of recent developments in the theory of positive solutions for boundary value problems, written by two of the world's leading researchers in the area. Book jacket.
9780128036525 English 0128036524 Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditionsDiscusses second order difference equations with multi-point boundary conditionsIntroduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions, In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of maths as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions, The book contains the study of the existence, multiplicity, and nonexistence of positive solutions of several classes of boundary value problems for nonlinear systems of ordinary differential equations, difference equations, and fractional equations. The first two chapters are devoted to systems of nonlinear second-order or higher-order ordinary differential equations with Riemann-Stieltjes boundary conditions. Systems of nonlinear second-order difference equations subject to multi point boundary conditions are investigated in the third chapter. The last two chapters cover systems of nonlinear Riemann-Liouville fractional differential equations with either uncoupled or coupled integral boundary conditions. Various classes of systems - namely, systems with parameters or without parameters, systems with nonsingular or singular nonlinearities, and systems with sign-changing nonlinearities û are studied. In each chapter, various examples are presented which support the main results. Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions provides a comprehensive description of recent developments in the theory of positive solutions for boundary value problems, written by two of the world's leading researchers in the area. Book jacket.