Resonance problems for the one-dimensional 𝑝-Laplacian

Drábek, Pavel; Robinson, Stephen

doi:10.1090/S0002-9939-99-05485-4

Resonance problems for the one-dimensional $p$-Laplacian
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by Pavel Drábek and Stephen B. Robinson

Proc. Amer. Math. Soc. 128 (2000), 755-765

DOI: https://doi.org/10.1090/S0002-9939-99-05485-4

Published electronically: September 9, 1999

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Abstract:

We consider resonance problems for the one dimensional $p$-Laplacian, and prove the existence of solutions assuming a standard Landesman-Lazer condition. Our proofs use variational techniques to characterize the eigenvalues, and then to establish the solvability of the given boundary value problem.

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