Strongly indefinite systems with critical Sobolev exponents

Hulshof, Josephus; Mitidieri, Enzo; vanderVorst, Robertus

doi:10.1090/S0002-9947-98-02159-X

Strongly indefinite systems with critical Sobolev exponents
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by Josephus Hulshof, Enzo Mitidieri and Robertus vanderVorst

Trans. Amer. Math. Soc. 350 (1998), 2349-2365

DOI: https://doi.org/10.1090/S0002-9947-98-02159-X

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Abstract:

We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.

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