THE DIRICHLET PROBLEMS OF A CLASS OF SEMILINEAR EQUATIONS

In this paper we proved the exstence of solutions to the following Diriehlet problem: \left\\beginarrayl-\left(\frac\Delta2+\mu\right) u+f(u)=\nu, \quad \text in D, \\ \left.u\right|_\partial D=g,\endarray\right. where D is a bounded regular domain of R^d,μ and v are signed measures belonging to the generalizead Kato class GK_d,f is a continuously differentiable function on R¹,g is a continuous function on \partial D.The main tools are Dirichlet forms and Markov processes.