Geodesic
The Stability of a Functional Analogue of the Wave Equation
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 376-385

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For h € R and φ : R2 → R define Lhφ: R2 → R by (Lhφ)(x, y) = φ (x + h, y) + φ (x — h,y) — φ (x,y + h) — φ (x,y — h) for all (x,y) € R2. The aim of the paper is to establish the following "stability" theorem concerning the functional equation if δ > 0, f : R2 → R and then there exists ɛ > 0 ami φ : R2 → R such that (Lhφ)(x, y ) = 0 for all x, y,h ∊ R and
DOI : 10.4153/CMB-1990-062-3
Mots-clés : 39B40D, 39B50, 39A11 
Bean, Michael. The Stability of a Functional Analogue of the Wave Equation. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 376-385. doi: 10.4153/CMB-1990-062-3
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     author = {Bean, Michael},
     title = {The {Stability} of a {Functional} {Analogue} of the {Wave} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {376--385},
     year = {1990},
     volume = {33},
     number = {4},
     doi = {10.4153/CMB-1990-062-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-062-3/}
}
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