Computing the first eigenpair of the p-Laplacian in annuli

Ercole, Grey; Santo, Júlio César do Espírito; Martins, Eder Marinho

doi:10.1016/j.jmaa.2014.09.016

Cited by 3 publications

(3 citation statements)

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“…Hence, (13) implies that A( w), w = w p−1 X w X and then (A2) leads us to conclude that w = w (note that w X = w X = µ). Thus, (12) yields…”

Section: The Results Of Convergencementioning

confidence: 99%

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Solving an Abstract Nonlinear Eigenvalue Problem by the Inverse Iteration Method

Ercole

2018

Bull Braz Math Soc, New Series

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Let (X, · X ) and (Y, · Y ) be Banach spaces over R, with X uniformly convex and compactly embedded into Y. The inverse iteration method is applied to solve the abstract eigenvalue problemKeywords: Eigenvalue problems, inverse iteration, quasilinear elliptic equations.with the equality occurring whenever u = tv, for some t ≥ 0;(AB) for each w ∈ Y \ {0} given, there exists at least one u ∈ X \ {0} such thatWe observe from (A1) and (B1) that (1) is homogeneous, that is: if (λ, w) solves (1) the same holds true for (λ, tw) , for all t = 0. Motivated by this intrinsic property of eigenvalue problems, we say that λ is an eigenvalue of (1) and that w is an eigenvector of (1) corresponding to λ or, for shortness, we simply say that (λ, w) is an eigenpair of (1).Hypotheses (A2) and (B2) imply, respectively, that

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“…Hence, (13) implies that A( w), w = w p−1 X w X and then (A2) leads us to conclude that w = w (note that w X = w X = µ). Thus, (12) yields…”

Section: The Results Of Convergencementioning

confidence: 99%

“…for a general bounded domain and presented some numerical experiments for the unit square as motivation to their conjecture. The approach used in [4], based on radial symmetry, was adapted in [12] to obtain the pair (λ p , u p ) for a radially symmetric annulus.…”

Section: Introductionmentioning

confidence: 99%

Solving an Abstract Nonlinear Eigenvalue Problem by the Inverse Iteration Method

Ercole

2018

Bull Braz Math Soc, New Series

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“…Hence, our approach is to construct the test function from a numerical approximation of the principal eigenfunction. In one dimension we use the shooting method, in higher dimensions there are numerous effective algorithms for various domains -see, e.g., [5,6,7,8,9,10,11,15]. But, we have to be careful when inserting the numerical solution into (1.3) and (1.4).…”

Section: Introductionmentioning

confidence: 99%

Numeric estimates of the principal eigenvalue of the p-Laplacian using interval arithmetic

Benedikt

Půlpán

2023

ejde

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We present a numerical algorithm for computing rigorous upper and lower estimates of the principal eigenvalue of the p-Laplacian. To control all possible errors including the rounding errors of the computer arithmetic, we use the interval arithmetic. We implement our algorithm in the Julia programming language using IntervalArithmetic.jl package [12]. See also https://ejde.math.txstate.edu/special/02/b3/abstr.html

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