A note on solutions of semilinear equations at resonance in a cone

Volume 58 / 1993

Bogdan Przeradzki Annales Polonici Mathematici 58 (1993), 95-103 DOI: 10.4064/ap-58-1-95-103


A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).


  • Bogdan Przeradzki

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