By I. Todhunter
This quantity is made from electronic pictures from the Cornell college Library ancient arithmetic Monographs assortment.
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Extra info for An elementary treatise on the theory of equations: with a collection of examples.
3) holds, but also in the further parameter set m−1 m−3 m−3 m > 2, p < s, < s < m − 1, 1+ s
0 is sufficiently small, depending only on m and s. 2. 6), with β < α < γ, is degenerate at t = 0 for values m = 2 (since v (0) = 0) and is also singular in case q(0) = 0. Accordingly, local existence and uniqueness of solutions of this initial value problem requires demonstration. We make the assumptions (Q1), (Q3) and (F 1), (F 2) and (F 5). Actually we do not use the full strength of either (F 2) or (F 5).
0 M Indeed for v ∈ C we have t0 T [v] − α ∞ s ≤ 0 0 q(τ ) f (v(τ ))dτ q(s) 1/(m−1) ds ≤ 1 m 1/(m−1) t M ≤ε m 0 32 ´ P. PUCCI, M. GARC´IA-HUIDOBRO, R. MANASEVICH, AND J. SERRIN and in turn T [v] ∈ C. Hence T (C) ⊂ C. Let (vk )k be a sequence in C and let s, t be two points in [0, t0 ]. Then 2 ¯m 1/(m−1) t M |t − s|. |T [vk ](t) − T [vk ](s)| ≤ m By the Ascoli-Arzel`a theorem this means that T maps bounded sequences into relatively compact sequences with limit points in C, since C is closed. 6), and so T [vk ] tends to T [v] pointwise in [0, t0 ] as k → ∞.
Math. , 47 (1998), 529-539.  P. Pucci and J. Serrin, The strong maximum principle revisited, J. Diff. Equations, 196 (2004), 1-66.  J. Serrin and M. Tang, Uniqueness of ground states for quasilinear elliptic equations, Indiana Univ. Math. , 49 (2000), 897-923  K. Tso, On symmetrization and Hessian operators, J. d’Anal. Math. 52 (1989), 94-106. it ´tica, Universidad Cato ´ lica de Chile, Casilla 306, Correo 22, SanDepartamento de Matema tiago, Chile.
An elementary treatise on the theory of equations: with a collection of examples. by I. Todhunter