This paper examines the existence and nonexistence of solutions on the Cauchy problem for the evolutionary p-Laplacian equation with nonlocal source. By a priori estimates, we establish the local existence, global existence and nonexistence of solutions for that Cauchy problem. In particular, a Fujita's type critical exponent is obtained, which extends several classical results to the problem considered here.

中文翻译：

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具有非局部来源的演化p-Laplacian方程的局部和全局存在

本文研究了具有非局部源的演化p-Laplacian方程的柯西问题的解的存在和不存在。通过先验估计，我们可以确定该柯西问题的解的局部存在，全局存在和不存在。特别是，获得了藤田类型的临界指数，这将几个经典结果扩展到此处考虑的问题。