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Nontrivial solutions of elliptic boundary value problems with resonance at zero. (English) Zbl 0572.35037
This interesting paper deals with equilibria of a general non-linear parabolic bounday value problem. The author uses Conley’s homotopy index theory to obtain the existence of equilibria of the parabolic equation (i.e. solutions of the corresponding elliptic equation) and gets even some results about the dynamics of the parabolic problem. These results generalize an earlier paper of H. Amann and E. Zehnder [Ann. Sc. Norm. Super. Pisa Cl. Sci., IV Ser. 7, 539-603 (1980; Zbl 0452.47077)].

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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