Nonlinear Functional Analysis of Boundary Value Problems 2013

Yong Hong Wu,Shaoyong Lai,Benchawan Wiwatanapataphee,Lishan Liu

doi:10.1155/2014/754976

Abstract

and Applied Analysis 3 solve a class of boundary value problems for second-order singular differential equations. (iii) In the paper titled “Existence and uniqueness of solution to nonlinear boundary value problems with sign-changing Green’s function,” by using the cone theory and the Banach contraction mapping principle, some existence and uniqueness results are established for a nonlinear higher-order differential equation boundary value problem with signchanging Green’s function. (iv) In the paper titled “Onboundedness and attractiveness of nonlinear switched delay systems,” the authors study the boundedness and attractiveness problems for a class of nonlinear switched delay systems. Some sufficient conditions are established to guarantee the system’s boundedness. The authors also work out the region where the solution will remain and the relationship between the initial function and the bounded region. (v) In the paper titled “Unbounded solutions of asymmetric oscillator,” the authors establish sufficient conditions for the existence of unbounded solutions of a nonlinear differential equation with a continuous, bounded, and periodic source function. (6) Stochastic Differential Equation Models (i) In the paper titled “A stochastic string with a compound poisson process,” the authors introduce a compound Poisson process with a constant jump intensity and random jump-size to capture information burst and the resulting discontinuous path and derive the no-arbitrage condition on the drift of instantaneous forward rates in the compound model. With the proposedmodel, the impact of random jump on the price of the zero coupon bond is shown in the paper. (ii) In the paper titled “Equilibrium asset and option pricing under jump diffusion model with stochastic volatility,” the authors study the equity premium and option pricing under a jump-diffusion model with stochastic volatility. The pricing kernel is established and the exact expression for the option price is derived by using the Fourier transformation method. (7) Fixed-Point Theory (i) In the paper titled “Generalizations of fixed-point theorems of Altman and Rothe types,” the authors present some extensions of the Altman and Rothe type fixed-point theorems. Some new fixed-point theorems for continuous operators are established by use of the theory of topological degree. (ii) In the paper titled “Commonfixed-points for weak contractive mappings in ordered metric space with applications,” the authors establish some new common fixed-point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. Yong Hong Wu Lishan Liu Benchawan Wiwatanapataphee Shaoyong Lai Submit your manuscripts at http://www.hindawi.com Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Problems in Engineering Hindawi Publishing Corporation http://www.hindawi.com Differential Equations International Journal of Volume 2014 Applied Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Probability and Statistics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Physics Advances in Complex Analysis Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Optimization Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Combinatorics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Operations Research Advances in

Highlights

(1) Well Posedness of Partial Differential Equation Boundary Value Problems (i) In the paper titled “Nonexistence results for the Schrodinger-Poisson equations with spherical and cylindrical potentials in R3,” the authors study a Schrodinger-Poisson system leading to the development of two theorems giving two regions on the parameter plane where the system has no nontrivial solutions
(2) Asymptotic and Stability Properties of Solutions (i) In the paper titled “On the L1 stability to a generalized Degasperis-Procesi equation,” by assuming that the strong solutions of the equation are bounded in the sense of L1(R)norm and the initial data is in the space L1(R) ∩ L2(R), the authors prove that the solutions are stable in the space L1(R)
The asymptotic behaviour of the global solutions is established and it is found that approximation of the global solutions can be obtained by solving the corresponding linear equation as time tends to infinity

Summary

Introduction

(iii) In the paper titled “Several dynamic properties of solutions to a generalized Camassa-Holm equation,” the author investigates some dynamic properties of strong solutions for a generalized Camassa-Holm equation. (1) Well Posedness of Partial Differential Equation Boundary Value Problems (i) In the paper titled “Nonexistence results for the Schrodinger-Poisson equations with spherical and cylindrical potentials in R3,” the authors study a Schrodinger-Poisson system leading to the development of two theorems giving two regions on the parameter plane where the system has no nontrivial solutions.

Results

Conclusion