一类拟线性椭圆方程3个非平凡解的存在性

The Existence of Three Nontrivial Solutions for a Class of Quasi-Linear Elliptic Equations

通过截断技术和涉及第二形变引理的变分方法研究了一类不含任何增长条件的拟线性椭圆方程3个非平凡解的存在性.首先利用截断技术和变分技巧得到该类拟线性椭圆方程存在1个非负非平凡解和1个非正非平凡解,然后通过第二形变引理构造这两个非平凡解之间的特殊山路,最后应用山路引理获得该类拟线性椭圆方程第三个非平凡解的存在性.

Using the truncation technique and the variational approach involving the second deformation lemma, the existence of three nontrivial solutions for a class of quasi-linear elliptic equations without any growth conditions is obtained. First, through the truncation technology and the variational technique, we obtain that the elliptic equations have a nonnegative nontrivial solution and a nonpositive nontrivial solu- tion. Subsequently, we use the second deformation lemma to construct a special mountain pass path be- tween the two nontrivial solutions and obtain the existence of a third nontrivial solution by the mountain pass lemma.