A boundary value problem on the whole line to second order nonlinear differential equations

作者：Philos Christos G^*; Purnaras Ioannis K

来源：Georgian Mathematical Journal, 2010, 17(2): 373-390.

DOI：10.1515/GMJ.2010.014

• Nonlinear differential equation
• boundary value problem on the whole line
• existence of solutions
• existence and uniqueness of solutions
• Schauder theorem
• Banach contraction principle

Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden-Fowler type and to the special case of second order linear ordinary differential equations, respectively.

• 出版日期2010