Unbounded solutions of asymmetric oscillator (Q2015240)

Summary: We obtain sufficient conditions for the existence of unbounded solutions of the nonlinear differential equation \[ (\varphi_p(x'))'+(p-1)[\alpha\varphi_p(x^+)-\beta\varphi_p(x^+)-\beta\varphi_p(x^-)]=/p-1(f(t,x,x'), \] where \(\varphi_p(u)=|u|^{p-2}u\), \(p>1\), \(x^+=\max\{x,0\}\), \(x^-=\max\{-x,0\}\), \(\alpha\), \(\beta\) are positive constants, and \(f\) is continuous, bounded, and \(T\)-periodic in \(t\) for some \(T>0\).