Portal de Periódicos da CAPES

Necessary and Sufficient Condition for Maintaining Oscillations and Nonoscillations in General Functional Equations and Their Asymptotic Properties

1979; Society for Industrial and Applied Mathematics; Volume: 10; Issue: 1 Linguagem: Inglês

10.1137/0510002

1095-7154

Bhagat Singh,

Advanced Mathematical Modeling in Engineering

A necessary and sufficient condition is found for the nonoscillation of \[\left( {r(t)y'(t)} \right)^{(n - 1)} + F(h(y(g(t))),t) = 0,\quad n \geqq 2.\] Case study for the asymptotic oscillatory behavior of solutions of the equations \[\left( {r(t)y'(t)} \right)^\prime + a(t)h(y(g(t))) = f(t)\] and \[\left( {r(t)y'(t)} \right)^\prime + p(t)y(t) + a(t)h(y(g(t))) = f(t)\] is made for the two cases when $\int ^\infty {{1 /{r(t)}}} \,dt = \infty $ and \[\int ^\infty { {1 /{r(t)}}} \,dt < \infty ,\quad r(t) > 0.\]