一类非线性Dirichlet问题的多重解

Multiplicity Results of a Class of Nonlinear Eigenvalue Dirichlet Problems

对一类具有p-Laplace算子的拟线性微分方程特征值Dirichlet问题采用变分法和Ricceri三临界点定理进行了探讨,在一些更易验证的条件下,证明了其在W01,p([a,b])上至少3个弱解存在的充分条件,这也从研究方法上推广了现有文献的结果.而且,作为应用,还给出了一个例子说明文中结论的正确性.

In this paper,the eigenvalue Dirichlet problem for a class of quasilinear differential equation with p-Laplace operator is studied by utilizing variational method and Ricceri three critical points theorem.Sufficient condition to guarantee the existence of at least three weak solutions in W1,p0（） are proved under some conditions which are easier to be verified.Some results in the recent literatures are generalized.Moreover,as an application,an example to illustrate the results is given also.