科研之友
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摘要
We consider the non-homogeneous critical semilinear elliptic problems %26lt;br%26gt;-Delta u+kappa u=u((N+2)/(N-2))+lambda f in Omega, %26lt;br%26gt;where Omega is a bounded smooth domain in R-N, f is an element of H-1(Omega), f %26gt;= 0 in Omega,kappa is an element of R is a fixed constant, and lambda %26gt; 0 is a parameter. We investigate the multiplicity of positive solutions to the problem and find the phenomenon depending on the space dimension N. Precisely, we show that the situation is drastically different between the cases N = 3, 4, 5 and N %26gt;= 6 if kappa %26gt; 0. Our proofs are based on the variational methods and Pohozaev type argument.
- 出版日期2012-1
