In this paper,we consider the following Kirchhoff-Schrodinger system with weakly attractive potentials:{-(a+b∫_(R)^(N)|▽u_(2)|^(2)△u_(2)+V_(2)u_(2)=λ_(2)u_(2)+v_(2)|u_(2)|^(p2-2)u_(2)+ap_(2)|u_(1)|^(q1)|u_(2)|^(q2...In this paper,we consider the following Kirchhoff-Schrodinger system with weakly attractive potentials:{-(a+b∫_(R)^(N)|▽u_(2)|^(2)△u_(2)+V_(2)u_(2)=λ_(2)u_(2)+v_(2)|u_(2)|^(p2-2)u_(2)+ap_(2)|u_(1)|^(q1)|u_(2)|^(q2-2)u_(2)/1(a+b∫_(R^(N))|▽u_(1)|^(2)dx)△u_(1)+V_(1)+u_(1)=λ_(1)u_(1)+v_(1)|u_(1)|^(p1-2)u_(1)+aq_(1)|u1|^(q1-2)u_(1)|u_(2)|^(q2),having prescribed mass∫_(R^(N))|u_(i)|^(2)dx=m_(i),where a>0,b,a,v_(i)>0,q_(i)>1,N=2,3,λ_(i)∈R are Lagrange multiplier and V_(i)∈C^(1)(R^(N))are potential functions for i=1,2.When 2+N/8<q1+q2<2^(*) and(p1,p2)∈R^(2),we prove the existence of multiple solutions,which are positive radial vectors.2^(*)=2N(N−2)is the Sobolev critical exponent.The proof is based on variational techniques and constrained minimization arguments.展开更多
文摘In this paper,we consider the following Kirchhoff-Schrodinger system with weakly attractive potentials:{-(a+b∫_(R)^(N)|▽u_(2)|^(2)△u_(2)+V_(2)u_(2)=λ_(2)u_(2)+v_(2)|u_(2)|^(p2-2)u_(2)+ap_(2)|u_(1)|^(q1)|u_(2)|^(q2-2)u_(2)/1(a+b∫_(R^(N))|▽u_(1)|^(2)dx)△u_(1)+V_(1)+u_(1)=λ_(1)u_(1)+v_(1)|u_(1)|^(p1-2)u_(1)+aq_(1)|u1|^(q1-2)u_(1)|u_(2)|^(q2),having prescribed mass∫_(R^(N))|u_(i)|^(2)dx=m_(i),where a>0,b,a,v_(i)>0,q_(i)>1,N=2,3,λ_(i)∈R are Lagrange multiplier and V_(i)∈C^(1)(R^(N))are potential functions for i=1,2.When 2+N/8<q1+q2<2^(*) and(p1,p2)∈R^(2),we prove the existence of multiple solutions,which are positive radial vectors.2^(*)=2N(N−2)is the Sobolev critical exponent.The proof is based on variational techniques and constrained minimization arguments.
