MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER

作者：Wang Youjun^*; Shen Yaotian

来源：Acta Mathematica Scientia, 2010, 30(1): 113-124.

DOI：10.1016/S0252-9602(10)60027-6

• nonlinear elliptic equation
• critical potential
• linking

Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order Sobolev-Hardy space, we obtain the existence of sign-changing solutions for the nonlinear elliptic equation
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where 0 is an element of Omega subset of B(alpha)(0) subset of R(N), N >= 3, ln((i)) = Pi(i)(j=1) ln((j)), and R = ae((k-1)), where e((0)) = 1, j=1 e((j)) = e(e(j-1)) for j >= 1, ln((1)) = ln, ln((j)) = ln ln((j-1)) for j >= 2. Besides, positive and negative solutions are obtained by a variant mountain pass theorem.

• 出版日期2010-1
• 单位华南理工大学