Interval criteria for forced oscillation of differential equations with \(p\)-Laplacian and nonlinearities given by Riemann-Stieltjes integrals (Q2914423)

The authors consider forced second-order differential equations with \(p\)-Laplacian and nonlinearities given by a Riemann-Stieltjes integral in the form of NEWLINE\[NEWLINE (p(t)\phi_{\gamma}(x'(t)))'+q_0(t)\phi_{\gamma}(x(t))+\int_0^bq(t,s)\phi_{\alpha(s)}(x(t))d\zeta(s)=e(t), NEWLINE\]NEWLINE where \(\phi_{\alpha}(u):=| u|^{\alpha}\text{sgn}u\), \(\gamma,b\in(0,\infty)\), \(\alpha\in C[0,b)\) is strictly increasing such that \(0\leq \alpha(0)<\gamma<\alpha(b)\), \(p,q_0,e\in C([0,\infty),\mathbb R)\) with \(p(t)>0\) on \([t_0,\infty)\), \(q\in C[0,\infty)\times [0,b)\), and \(\zeta :[0,b)\to \mathbb R\) is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained.