On a new class of elliptic systems with nonlinearities of arbitrary growth

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We gua rantee the existence of infinitely many different pairs of solutions to the system. {-Δ,u=vp in Ω; -Δv=f(u) in Ω; u=v=0 on ∂Ω, where 0

N and the continuous nonlinear term f has an unusual oscillatory behavior. The sequence of solutions tends to zero (resp., infinity) with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity (resp., at zero) whenever f oscillates near zero (resp., at infinity). Our results provide the first applications of Ricceri's variational principle in the theory of coupled elliptic systems.

Original languageEnglish
Pages (from-to)1917-1928
Number of pages12
JournalJournal of Differential Equations
Volume249
Issue number8
DOIs
Publication statusPublished - Oct 2010

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Elliptic Systems
Infinity
Nonlinearity
Zero
Arbitrary
Term
Variational Principle
Coupled System
Tend
Norm
Class

Keywords

  • Elliptic systems
  • Nonlinearities of arbitrary growth
  • Ricceri's variational principle

ASJC Scopus subject areas

  • Analysis

Cite this

On a new class of elliptic systems with nonlinearities of arbitrary growth. / Kristály, A.

In: Journal of Differential Equations, Vol. 249, No. 8, 10.2010, p. 1917-1928.

Research output: Contribution to journalArticle

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AB - We gua rantee the existence of infinitely many different pairs of solutions to the system. {-Δ,u=vp in Ω; -Δv=f(u) in Ω; u=v=0 on ∂Ω, where 0N and the continuous nonlinear term f has an unusual oscillatory behavior. The sequence of solutions tends to zero (resp., infinity) with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity (resp., at zero) whenever f oscillates near zero (resp., at infinity). Our results provide the first applications of Ricceri's variational principle in the theory of coupled elliptic systems.

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