一类带Hardy项和Sobolev临界指数的椭圆型方程正解的存在性
The Existence of a Positive Solution for an Elliptical Equation with Hardy Terms and Sobolev Critical Exponents
摘要: 本文研究了一类带Hardy项和Sobolev临界指数的椭圆型方程。通过变分法，我们得到了方程的能量泛函在零点附近存在局部极小值点，且该极小值点为方程的正解。此外，当方程的扰动项趋于零时，该正解也趋于零。
Abstract: The elliptical equation with Hardy terms and Sobolev critical exponents is studied. By the variational methods, we have obtained that there exists a local minimum point of the energy functional related to the equation which is near zero, and the local minimum point is a positive solution of this equation. Moreover, this positive solution tends to zero when the perturbed term goes to zero.
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