Boundedness of solutions for nonlinear reversible system at resonance (Q596699)

Sufficient conditions for the existence of bounded and unbounded solutions of the second-order differential equation \[ (\varphi_p(x'))'+ (p-1) n^p\varphi_p(x)+ f(x)\varphi_p(x')+ g(x)= e(t) \] are derived, where \(\varphi_p(u)=| u|^{p-2} u\), \(p\geq 2\), \(n\in\mathbb{N}\), \(f,g\in C^\infty(\mathbb{R})\) are odd and \(e(t)\in C^\infty(\mathbb{R})\) is odd.