In this paper,we consider the fractional critical Schrödinger equation(FCSE)(-Δ)^(s)u-|u|2^(*)s-2 u=0,where u∈˙H^(s)(R^(N)),N≥4,0<s<1 and 2^(*)s=2 N/N-2 s is the critical Sobolev exponent of order s.By ...In this paper,we consider the fractional critical Schrödinger equation(FCSE)(-Δ)^(s)u-|u|2^(*)s-2 u=0,where u∈˙H^(s)(R^(N)),N≥4,0<s<1 and 2^(*)s=2 N/N-2 s is the critical Sobolev exponent of order s.By virtue of the variational method and the concentration compactness principle with the equivariant group action,we obtain some new type of nonradial,sign-changing solutions of(FCSE)in the energy space˙H^(s)(R^(N)).The key component is that we take the equivariant group action to construct several subspace of˙H^(s)(R^(N))with trivial intersection,then combine the concentration compactness argument in the Sobolev space with fractional order to show the compactness property of Palais-Smale sequences in each subspace and obtain the multiple solutions of(FCSE)in˙H^(s)(R^(N)).展开更多
基金supported by National Key Research and Development Program of China(No.2020YFA0712900)NSFC(No.112371240 and No.12431008)supported by NSFC(No.12001284)。
文摘In this paper,we consider the fractional critical Schrödinger equation(FCSE)(-Δ)^(s)u-|u|2^(*)s-2 u=0,where u∈˙H^(s)(R^(N)),N≥4,0<s<1 and 2^(*)s=2 N/N-2 s is the critical Sobolev exponent of order s.By virtue of the variational method and the concentration compactness principle with the equivariant group action,we obtain some new type of nonradial,sign-changing solutions of(FCSE)in the energy space˙H^(s)(R^(N)).The key component is that we take the equivariant group action to construct several subspace of˙H^(s)(R^(N))with trivial intersection,then combine the concentration compactness argument in the Sobolev space with fractional order to show the compactness property of Palais-Smale sequences in each subspace and obtain the multiple solutions of(FCSE)in˙H^(s)(R^(N)).
