A non resonance under and between the two first eigenvalues in a nonlinear boundary problem

Anane, Aomar; Chakrone, Omar; Moradi, Najat

doi:10.5269/bspm.v28i2.11338

Cited by 1 publication

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“…Throughout this subsection, we work on gathering needed properties to apply a version of the classical "Mountain Pass Theorem" for a C 1 functional restricted to a C 1 manifold (see [1,8]). Our purpose is of course to obtain existence results for (P f ) and by doing so, extend some of the known results in [4,5,7]. In order to have things well defined in the context of variational approach, we consider for u ∈ W 1,p (Ω),…”

Section: Nonresonance Between the First Two Eigenvaluesmentioning

confidence: 99%

“…The problem was actually considered recently in [7] for the p-Laplacian operator (in the case V ≡ 0), where the existence of the p-harmonic solutions was proved. Also in [5], the case V ≡ 1 was treated under and between the first two eigenvalues. In the present paper, we shall adapt and extend the approach in [7] in order to We simply write ∆ instead of ∆ 2 and call the 2-Laplace operator simply Laplace operator.…”

Section: Introductionmentioning

confidence: 99%

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Weighted Steklov problem under nonresonance conditions

Doumatè

Marcos

2018

B Soc Paran Mat

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We deal with the existence of weak solutions of the nonlinear problem −∆pu + V |u| p−2 u = 0 in a bounded smooth domain Ω ⊂ R N which is subject to the boundary condition |∇u| p−2 ∂u ∂ν = f (x, u). Here V ∈ L ∞ (Ω) possibly exhibit both signs which leads to an extension of particular cases in literature and f is a Carathéodory function that satisfies some additional conditions. Finally we prove, under and between nonresonance conditions, existence results for the problem.

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