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Volume 7,     Number 3,     Fall 1999

 

MULTIPLICITY AND MORSE INDICES OF
SIGN-CHANGING SOLUTIONS FOR
SEMILINEAR EQUATIONS
PHILIP KORMAN AND TIANCHENG OUYANG

Abstract. We study Morse indices of sign-changing solutions for Dirichlet two-point problems. If solution has k interior roots, we show that its Morse index is equal to either k or k + 1, with a precise answer possible in some important cases. As an application we establish exact multiplicity of sign-changing solutions for two classes of problems, which arise in population modeling.

 

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