We study the periodic boundary value problem associated with the φ-Laplacian equation of the form (φ(u'))'+f(u)u'+g(t,u)=s, where s is a real parameter, f and g are continuous functions and g is T-periodic in the variable t. The interest is in Ambrosetti–Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter s. We investigate this problem for a broad family of nonlinearities, under local coercivity conditions on g. As a consequence, we generalize, in a unified framework, various classical and recent results on parameter-dependent nonlinear equations.
Periodic solutions to parameter-dependent equations with a φ-Laplacian type operator
FELTRIN, GUGLIELMO;Zanolin, Fabio
2018-01-01
Abstract
We study the periodic boundary value problem associated with the φ-Laplacian equation of the form (φ(u'))'+f(u)u'+g(t,u)=s, where s is a real parameter, f and g are continuous functions and g is T-periodic in the variable t. The interest is in Ambrosetti–Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter s. We investigate this problem for a broad family of nonlinearities, under local coercivity conditions on g. As a consequence, we generalize, in a unified framework, various classical and recent results on parameter-dependent nonlinear equations.File in questo prodotto:
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