Existence and Nonexistence of Solutions of Nonlinear Dirichlet Problems with First Order Terms

Authors: Moschini L.¹; Pohozaev S.I.²; Tesei A.³

Source: Journal of Functional Analysis, Volume 177, Number 2, November 2000 , pp. 365-382(18)

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Abstract:

Existence theorems for nonnegative solutions to a class of nonlinear Dirichlet problems with first order terms are proved. Nonexistence results are also discussed, depending on the regularity of the coefficient of the first order term. The proofs make use of a direct variational approach and of integral identities. Copyright 2000 Academic Press.

Keywords: Dirichlet problems; first order terms; existence of solutions; nonexistence of solutions; problems of indefinite type; nonnegative solutions

Language: English

Document Type: Research article

Affiliations: 1: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, Rome, I-00185, Italy 2: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, Moscow, 117966, Russia 3: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, Rome, I-00185, Italy

Publication date: 2000-11-01