On the Morse critical groups for indefinite sublinear elliptic problems (Q1863614)

The author studies a parameter dependent semilinear Dirichlet problem with weight by methods of infinite dimensional Morse theory. Specifically, it is shown that, if a parameter in the problem is not too large, the Morse critical groups at zero for the associated energy functional are trivial. This implies the existence of a nontrivial solution when some nonlinear term in the problem is asymptotically linear. Then the bifurcation of small solutions is obtained under the assumption that a parameter related to the weight is sufficiently small.