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Potential bounds in problems on quasilinear elliptic equations
Author(s) -
Krasnosel'Skii Mark,
Mennicken Reinhard,
Rachinskii Dmitrii
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.1999.3212070107
Subject(s) - mathematics , nonlinear system , boundary value problem , order (exchange) , quarter period , elliptic operator , elliptic curve , mathematical analysis , physics , finance , quantum mechanics , economics
We study quasilinear elliptic equations with strong nonlinear terms and systems of such equations. The methods developed by the authors in [1], [2] are used to prove the existence of solutions for boundary—value problems using some information on behavior of potential bounds for nonlinearities; the L–characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classical solutions of quasilinear second order elliptic equations.