Vol. 55, No. 1, pp. 1-9 (1998)
Remarks on Nagumo's Condition
Philip KormanDepartment of Mathematical Sciences, University of Cincinnati,
Cincinnati, Ohio 45221-0025 - USA
Abstract: For quasilinear elliptic equations it is commonly assumed that nonlinearity grows not faster than quadratically in the gradient of solution. This assumption is necessary in order to get an a priori bound on the gradient of solution, which is a part of most existence proofs. However, it appears that this condition is not essential for existence of solution, only different techniques of proof are needed in its absence.
Keywords: Existence of solutions; Nagumo's condition.
Classification (MSC2000): 34B15, 35J60
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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.