Perturbed neumann problems with many solutions

Research output: Contribution to journalArticle

Abstract

Given f, g:[0,∞)→ ℝ two continuous nonlinearities with f(0)=g(0)=0 and f having a suitable oscillatory behavior at zero or at infinity, we prove by a direct method that for every k€ℕ, there exists ∞k > 0 such that the problem [image omitted] has at least k distinct nonnegative weak solutions in W1,p (Ω) whenever |∞|. We also give various W1,p- and L-estimates of the solutions. No growth assumption on g is needed, and α € L (Ω) may be sign-changing or even negative depending on the rate of the oscillation of f.

Original languageEnglish
Pages (from-to)1114-1127
Number of pages14
JournalNumerical Functional Analysis and Optimization
Volume29
Issue number9-10
DOIs
Publication statusPublished - Sep 2008

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Neumann Problem
Direct Method
Weak Solution
Non-negative
Infinity
Nonlinearity
Oscillation
Distinct
Zero
Estimate

Keywords

  • Arbitrarily many solutions
  • Oscillatory nonlinearity
  • Perturbed Neumann problem

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization
  • Signal Processing
  • Computer Science Applications

Cite this

Perturbed neumann problems with many solutions. / Kristály, A.

In: Numerical Functional Analysis and Optimization, Vol. 29, No. 9-10, 09.2008, p. 1114-1127.

Research output: Contribution to journalArticle

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