带有变指数拟线性椭圆方程组的边界爆破解

摘要

The semilinear elliptic equations with variable exponents is studied in a smooth domain, and the equation systems verifies the conditions of boundary blow-up. Upon the basis of constant exponents, this paper takes into deep considerations of the case of variable exponents and obtains the existence, uniqueness and boundary behavior of boundary blow-up solutions in the critical and subcritical condition by the construction of super-sub solutions and interation method.%研究了在光滑有界域中带有变指数的拟线性椭圆方程组，且该方程组满足边界爆破的条件，在常指数的基础上进一步深入讨论了变指数的情况。主要运用了构造上下解和迭代的方法证明了边界爆破解在临界与次临界条件下，解的存在性，唯一性以及边界行为。