Almost-periodic solutions of a quasilinear system of partial differential equations
The author studies the existence and uniqueness of almost-periodic solutions of quasi-linear systems of differential equations with a small parameter. He considers the system \[ (1)\quad \partial^{n_ j}u_ j(x)/\partial x_ 0^{n_ j}+\sum_{r=1,...,m,s<n_ j,| s| \leq Q}a_ s^{jr}\partial^{| s|}u_ r(x)/\partial x_ 0^{s_ 0}...\partial x_ p^{s_ p}+\epsilon F_ j(u)=f_ j(x) \] where \(u=(u_ 1,...,u_ m)\), \(| s| =\sum^{p}_{\ell =0}s_{\ell}\), \(a_ s^{jr}=const.\), \(\sum^{m}_{j=1}n_ j=n\). \(\epsilon\) is a small parameter, \(F_ j\in C^{4Q+1}\) verifies a suitable boundedness assumption. By means of approximation methods he obtains some conditions for the existence of solutions of (1).
scientific article; zbMATH DE number 3889983