Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is shown that the second-order nonlinear differential equation (p(t)x^')^'+q(t)x=f(t,x,x^'),t>=0 has monotone positive solutions asymptotic to a prescribed nonprincipal solution v(t) at ~ of the corresponding linear homogeneous equation (p(t)x^')^'+q(t)x=0,t>=0, where p@?C([0,~),(0,~)), q@?C([0,~),R) and f@?C([0,~)xRxR,R). An example is given to illustrate the obtained result.
['Türker Ertem', 'A. Zafer']
I am writing a research paper on a idea Monotone positive solutions for a class of second-order nonlinear differential equations
[{"from": "human", "value": "I am writing a research paper on a idea Monotone positive solutions for a class of second-order nonlinear differential equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is shown that the second-order nonlinear differential equation (p(t)x^')^'+q(t)x=f(t,x,x^'),t>=0 has monotone positive solutions asymptotic to a prescribed nonprincipal solution v(t) at ~ of the corresponding linear homogeneous equation (p(t)x^')^'+q(t)x=0,t>=0, where p@?C([0,~),(0,~)), q@?C([0,~),R) and f@?C([0,~)xRxR,R). An example is given to illustrate the obtained result."}]