This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem - Au = Aa （x） u I u Iq- 2 ＋ b（x）u｜u｜2.-2 in a bounded domain coupled with...This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem - Au = Aa （x） u I u Iq- 2 ＋ b（x）u｜u｜2.-2 in a bounded domain coupled with Dirichlet boundary condition. Here 2＊ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Ne- hari manifold method we prove that one can find an interval A such that there exist at least two positive solutions of the problem for A E A.展开更多
文摘This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem - Au = Aa （x） u I u Iq- 2 ＋ b（x）u｜u｜2.-2 in a bounded domain coupled with Dirichlet boundary condition. Here 2＊ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Ne- hari manifold method we prove that one can find an interval A such that there exist at least two positive solutions of the problem for A E A.
