Boundedness and convergence to zero of solutions of a forced second-order nonlinear differential equation

Abstract Sufficient conditions for continuability, boundedness, and convergence to zero of solutions of ( a ( t ) x ′)′ + h ( t , x , x ′) + q ( t ) f ( x ) g ( x ′) = e ( t , x , x ′) are given.

[1]  J. Graef,et al.  Asymptotic behavior of solutions of a second order nonlinear differential equation , 1975 .

[2]  H. Arthur Dekleine.  Bounded Solutions for a Second Order Nonlinear Equation , 1971 .

[3]  Boundedness theorems for certain second order nonlinear differential equations , 1970 .

[4]  S. Londen.  Some Nonoscillation Theorems for a Second Order Nonlinear Differential Equation , 1973 .

[5]  Explicit bounds for solutions of certain second order nonlinear differential equations , 1967 .

[6]  J. Wong.  Remarks on Stability Conditions for the Differential Equation x″ + a(t)ƒ(x) = 0 , 1969, Journal of the Australian Mathematical Society.

[7]  R. Grimmer,et al.  On the asymptotic behavior of solutions of $x''+a(t)f(x)=e(t)$. , 1972 .

[8]  M. Hammett.  Nonoscillation properties of a nonlinear differential equation , 1971 .

[9]  J. Graef,et al.  Continuability, boundness and asymptotic behavior of solutions ofx″ +q(t)f(x)=r(t) , 1974 .

[10]  R. Grimmer.  On nonoscillatory solutions of a nonlinear differential equation , 1972 .

[11]  On boundedness of solutions of certain second-order differential equations☆ , 1969 .

[12]  V. Komkov.  Continuability and estimates of solutions of (a(t)ψ(x)x')' + c(t)f(x) = 0 , 1974 .

[13]  J. Wong.  Some Stability Conditions for $x'' + a( t )x^{2n - 1} = 0$ , 1967 .

[14]  A. Kartsatos,et al.  On the maintenance of oscillations of nth order equations under the effect of a small forcing term , 1971 .

[15]  J. Baker.  Stability Properties of a Second Order Damped and Forced Nonlinear Differential Equation , 1974 .

[16]  A. Kartsatos.  On positive solutions of perturbed nonlinear differential equations , 1974 .

[17]  R. Grimmer,et al.  Stability properties of(r(t)u′)′+a(t) f(u) g(u′)=0 , 1970 .