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Multiple solutions for resonant elliptic equations via local linking theory and Morse theory. (English) Zbl 0998.35021
The authors deal with the multiple solutions of the problem $$ \cases -\Delta u=g(x,u) \quad &\text{in }\Omega\\ u=0\quad &\text{on } \partial \Omega\endcases$$ where $g\in C^1(\overline \Omega\times \bbfR, \bbfR)$. They consider two classes of elliptic resonant problems, namely: a) double-double resonant case, b) the authors introduce some new conditions and compute the critical groups both at zero and at infinity precisely. Combined local linking theory and Morse theory, the authors present three solutions for the completely resonant case.

MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
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References:
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