unbounded solution

In this paper, we discuss the generalized Dirichlet problem for a class of nonlinear equations on unbounded domain by using probabilistic methods. Under certain conditions, we prove that the bounded solution to the Problem exists and is unique.

利用概率方法研究无穷区域上一类非线性方程的广义Dirichlet问题，在一定条件下，证明其有界解的存在唯一性。

The Sobolev interpolation inequality and prior estimate on time are applied to show the existence of solution in unbounded domain.

利用Sobolev插值不等式以及关于时间t的先验估计证明了该方程在无界域上解的存在性；

Second theorem shows that the existence of solution is possible under suitable conditions when the limit of growth of nonlinear term at infinity is an unbounded function.

第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解。