关于一类拟线性椭圆方程正解的存在性问题

Positive solution to a class of quasilinear elliptic equation on

讨论了拟线性椭圆方程-u″+u-k(u2)″u=f(x,u),x∈R(*),其中k>0是常数,f(x,u)是一个关于u的超线性和次临界函数,且f(x,0)=0.在函数f(x,u)满足某些条件下,通过变分法证明了方程(*)至少存在一个正解.

We discuss quasilinear elliptic equation -u″＋u-k（u^2）″u=f（x,u）,x∈R（＊）, Where k 〉 0 is a constant,f （x, u） is a superlinear and suberitical function in u and f（ x ,0） = 0. We prove the existence of solutions for （ ＊ ） under some hypothese on f（x, u） via variational methods.