Results 11 to 20 of about 1,211,085 (119)
On the Fredholm Alternative for the Fučík Spectrum
Abstract and Applied Analysis, 2010 We consider resonance problems for the one-dimensional p-Laplacian assuming Dirichlet boundary conditions. In particular, we consider resonance problems associated with the first three curves of the Fučík Spectrum.
Pavel Drábek, Stephen B. Robinson
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On the First Curve in the FučiK Spectrum with Weights for a Mixed p-Laplacian
International Journal of Mathematics and Mathematical Sciences, 2007 We show the existence of a first curve in the Fučik spectrum with weights for the p-Laplacian under mixed boundary conditions. We also study the asymptotic behavior of this first curve.
Liamidi Leadi, Aboubacar Marcos
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On the Fucik spectrum for elliptic systems
, 2006 We propose an extension of the concept of Fucik spectrum to the case of coupled systems of two elliptic equations, we study its structure and some applications. We show that near a simple eigenvalue of the system, the Fucik spectrum consists (after a suitable reparametrization) of two (maybe coincident) 2-dimensional surfaces.
E. Massa, B.Ruf
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Resonance problems with respect to the Fucik spectrum of the p-Laplacian [PDF]
Electronic Journal of Differential Equations, 2002 We solve resonance problems with respect to the Fucik spectrum of the $p$-Laplacian using variational methods.
Kanishka Perera
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Basisness of Fucik eigenfunctions for the Dirichlet Laplacian [PDF]
Electronic Journal of Differential Equations, 2022 We provide improved sufficient assumptions on sequences of Fucik eigenvaluesof the one-dimensional Dirichlet Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in \(L^2(0,\pi)\) .
Falko Baustian, Vladimir Bobkov
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Various Half‐Eigenvalues of Scalar p‐Laplacian with Indefinite Integrable Weights
Abstract and Applied Analysis, Volume 2009, Issue 1, 2009., 2009 Consider the half‐eigenvalue problem (ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0 a.e. t ∈ [0, 1], where 1 < p < ∞, ϕp(x) = |x|p−2x, x±(⋅) = max {±x(⋅), 0} for x ∈ 𝒞0 : = C([0, 1], ℝ), and a(t) and b(t) are indefinite integrable weights in the Lebesgue space ℒγ : = Lγ([0, 1], ℝ), 1 ≤ γ ≤ ∞.
Wei Li, Ping Yan, Pavel Drabek
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Generic properties of the Fucik spectrum of elliptic operators
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000 Given a bounded smooth domain Ω ⊂ Rn, n ≥ 2, and a second-order elliptic self-adjoint operator A on Ω, the set of points (α, β) ∈ R2 for which the problem Au = αu+ − βu- in Ω, u = 0 on ∂Ω (where u± = max{±u, 0}), has a non-trivial solution is called the Fucik spectrum of A.
Rynne, B. P.; id_orcid
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An extended variational characterization of the Fučík Spectrum for the p-Laplace operator
Calculus of Variations and Partial Differential Equations, 2020 The authors investigate the Fučík spectrum \(\Sigma\) of the \(p\)-Laplacian, i.e., pairs of parameters \(\alpha\) and \(\beta\) for which the zero Dirichlet problem for the equation \(-\Delta_p u = \alpha |u|^{p-2} u^+ - \beta |u|^{p-2} u^-\) in a bounded domain \(\Omega\) has a nontrivial solution.
Drábek, Pavel, Robinson, Stephen B.
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Electronic Journal of Differential Equations, 2018 In this article, we study the Fucik spectrum of the p-fractional Laplace operator with nonlocal normal derivative conditions which is defined as the set of all $(a,b)\in\mathbb{R}^2$ such that $$\displaylines{ \Lambda_{n,p}(1-\alpha)(-\Delta)_{p ...
Divya Goel +2 more
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The Fucik spectra for multi-point boundary-value problems
Electronic Journal of Differential Equations, 2010 We study the structure of the Fucik spectra for the linear multi-point differential operators. We introduce a variational approach in order to obtain a robust and global algorithm which is suitable for the exploration of unknown Fucik spectrum ...
Gabriela Holubova, Petr Necesal
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