Solvability of a one-dimensional quasilinear problem under nonresonance conditions on the potential

A. Marcos, Institut de Mathématiques et de Sciences Physiques, Porto Novo, Benin

E. J. Qualitative Theory of Diff. Equ., No. 57. (2009), pp. 1-29.

Abstract: Problem of the type $-\Delta_{p}u=f(u)+h(x) \textrm{ in } (a, b) $ with $u=0$ on $ \{a,b\} $ is solved under nonresonance conditions stated with respect to the first eigenvalue and the first curve in the Fu\v{c}ik spectrum of $(-\Delta_{p},W_{0}^{1,p}(a,b))$, only on a primitive of $f$.

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