带有变指数拟线性椭圆方程组的边界爆破解

Boundary blow up solution for variable exponent quasilinear elliptic systems

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.

The semilinear elliptic equations with variable exponents is studied in a smooth domain, and theequation systems verifies the conditions of boundary blow-up. Upon the basis of constant exponents, this papertakes into deep considerations of the case of variable exponents and obtains the existence, uniqueness andboundary behavior of boundary blow-up solutions in the critical and subcritical condition by the constructionof super-sub solutions and interation method.