Solutions of superlinear at zero elliptic equations via Morse theory (Q1130207)

For a semilinear elliptic Dirichlet problem, the author proves that all the Morse critical groups at zero are trivial, in the case where the nonlinear term is superlinear at zero. A similar calculation, where the nonlinear term is superlinear at infinity, has been obtained by \textit{Z. Q. Wang} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8, No. 1, 43-57 (1991; Zbl 0733.35043)]. Applications to multiple solution problems are studied via Morse theory.