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The computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue. (English) Zbl 0935.35055

The authors study the existence of a nontrivial solution of the elliptic problem which is of resonant type both at the origin and at infinity with the same higher eigenvalue and the nonlinear term is permitted to be unbounded. The main ingredient is the computation of the critical groups.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J70 Degenerate elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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