【摘要】 设L是线性自伴算子,N是非线性的并与L的谱满足一定的条件,考虑方程Lu-Nu=f(u)。本文使用Hilbert空间方法,有效地解决了如上非线形方程解的存在性,并且推广了文[1,2]的结论。另外,当"摄动项"f不依赖于u,且在有界集上充分小时,此问题有唯一解。更多还原

【Abstract】 Let L is a linear and self-adjoint operator while N is nonlinear and satisfies certain conditions relation to the spectrum of L.Consider the following equationLu-Nu=f(u).Using Hilbert space method,we effectively obtain the existence of solution to the above equation.Essentially,the main theorems ofare corollaries of our’s.Moreover,when the"forcing term"f is independent of u and small enough in some bounded set,the equation has a unique solution.更多还原