带变指标反应项的p-Laplacian方程解的爆破

Blow-up of Solutions to p-Laplacian Equations with Variable Exponents in Reaction Term

研究了有界区域上的带变指标反应项的p-Laplacian方程正解的爆破性质和整体存在性.通过构造适当的辅助函数,结合对空间区域的细致分析,利用特征函数法和不等式技巧,给出了其Dirichlet边值问题的正解产生爆破的充分条件.并利用上下解方法,证明了其整体解的存在性.

In this paper,we investigate the blow-up and global existence of positive solutions for p-Laplacian equations with variable exponents in the reaction term in bounded domain in RN.By constructing an appropriate auxiliary function,combining with a detailed analysis of the spatial region and using the eigenfunction method and its associated inequality characteristics,we obtain sufficient conditions for blow-up positive solutions of the equations with Dirichlet boundary conditions.By using the method of upper and lower solutions,we prove the existence of global solutions.