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Remarks on the resonant elliptic problem. (English) Zbl 1126.35319
Summary: We consider the semilinear elliptic equation $-\Delta u =f(x,u)$ with the Dirichlet boundary value for resonant nonlinearity at infinity. Using the Morse theory and perturbation method, some existence results of solution and multiple solutions are proved.

##### MSC:
 35J60 Nonlinear elliptic equations 35J25 Second order elliptic equations, boundary value problems 47J30 Variational methods (nonlinear operator equations) 58E05 Abstract critical point theory
Full Text:
##### References:
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