MULTIPLE SOLUTIONS FOR A SINGULAR SEMILINEAR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT AND SYMMETRIES

作者：Cano Alfredo^*; Hernandez Linares Sergio; Hernandez Martinez Eric

来源：Electronic Journal of Differential Equations, 2010, 112.

• Critical points
• critical Sobolev exponent
• multiplicity of solutions
• invariant under the action of a orthogonal group
• Palais-Smale condition
• singular semilinear elliptic problem
• relative category

We consider the singular semilinear elliptic equation -Delta u-mu/vertical bar x vertical bar(2)u-lambda u = f(x) vertical bar u vertical bar(2)*(-1) in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain, in R-N, N >= 4, 2* := 2N/N - 2 is the critical Sobolev exponent, f : R-N -> R is a continuous function, 0 < lambda < lambda(1), where lambda(1) is the first Dirichlet eigenvalue of - Delta - mu/vertical bar x vertical bar(2) in Omega and 0 < mu < (mu) over bar := (N-(2/2)(2). We show that if Omega and f are invariant under a subgroup of O(N), the effect of the equivariant topology of Omega will give many symmetric nodal solutions, which extends previous results of Guo and Niu [8].

• 出版日期2010-8-16