中文摘要：

考虑自然增长条件下一类拟线性椭圆型方程的非平凡解的存在性和不存在性．在以往的工作中，对此类方程的一个重要假设是自然增长项和未知函数的乘积是非负的，本文改进了此条件，把此条件推广到小于零的情况，得到使得方程解存在时自然增长项和未知函数的乘积的一个下界，并利用不光滑泛函的临界点定理证明了非平凡解的存在性．进一步，利用Pohozaev恒等式证明了当自然增长项和未知函数的乘积小于此下界时，方程不存在解，从而说明了此下界是最佳的．

英文摘要：

We consider the existence and nonexistence of nontrivial solution for quasilinear elliptic equation under natural growth condition. In the previous works on such equation, one of the important assumptions is that the product of the natural growth term and the unknown function is not less than zero. We improve this condition, extend it to the minus part and get the boundary below which such equation has nontrivial solution. We prove the existence of the nontrivial solution via nonsmooth critical point theory. Moreover, we use the Pohozaev identity to prove that the equation does not have any solution when the product of the natural growth term and the unknown function is less than this boundary, which means that this boundary is the best one.