关键词: 非线性, 边值问题, p-Laplace, 爆破

Abstract: The present paper studied the blow-up and boundedness of solutions at finite time for evolution p-Laplace equations with nonl inea r boundary conditions. The authors firstly proved a comparison principle in one dimension case and then found some conditions under which the solutions may bl ow-up at finite time. The authors also gave some conditions under which the sol utions will be bounded at any finite time. Similar results to the radial solutio ns of the equation in higher dimension case are also mentioned. In the last sect ion, a special example is presented to show that the theorems are applicable.

Key words: nonlinear, boundary value problem, p-Laplace, blow-up