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Comparison theorems for nonlinear ODE’s. (English) Zbl 0760.34030
The nonoscillatory solutions of the equation \((Lu(t)\equiv)L_ nu(t)+p(t)f[u(g(t))]=0\) have similar properties as those of the inequality \(Lu(t)\text{sgn} u[g(t)]\leq 0\) or \(Lu(t)\text{sgn} u[g(t)]\geq 0\). By means of that the equation \(L_ nu(t)+p(t)f[u(g(t))]=0\) is compared with the equation \(M_ nz(t)+q(t)h[z(r(t))]=0\). The linear equation is compared with the Euler equation.

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
Full Text: EuDML
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