We prove the solvability of the Dirichlet problem [formula], for every given h, under the following set of assumptions: [formula] and [formula] and [formula]. Here, λm and λm + 1 denote two consecutive higher eigenvalues of −Δ on H10(Ω) and G is the potential of g. Similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue λ1.
Nonresonance conditions on the potential for a semilinear elliptic problem
DEL SANTO, DANIELE;OMARI, PIERPAOLO
1994-01-01
Abstract
We prove the solvability of the Dirichlet problem [formula], for every given h, under the following set of assumptions: [formula] and [formula] and [formula]. Here, λm and λm + 1 denote two consecutive higher eigenvalues of −Δ on H10(Ω) and G is the potential of g. Similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue λ1.File in questo prodotto:
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