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Description
  • We treat a quasi-linear spectral problem at resonance with vanishing nonlinearity, satisfying certain orthogonality-related hypotheses. We first establish the boundedness of the set of all weak solutions in the Sobolev space, which then enables us to obtain an existence result by the Leray-Schauder degree theory. The boundedness is obtained from a very precise asymptotic estimate valid for large solutions which can be applied thanks to a sufficiently fast rate of decay of the nonlinearity.
  • We treat a quasi-linear spectral problem at resonance with vanishing nonlinearity, satisfying certain orthogonality-related hypotheses. We first establish the boundedness of the set of all weak solutions in the Sobolev space, which then enables us to obtain an existence result by the Leray-Schauder degree theory. The boundedness is obtained from a very precise asymptotic estimate valid for large solutions which can be applied thanks to a sufficiently fast rate of decay of the nonlinearity. (en)
Title
  • Perturbation of the p-Laplacian by vanishing nonlinearities (in one dimension)
  • Perturbation of the p-Laplacian by vanishing nonlinearities (in one dimension) (en)
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  • Perturbation of the p-Laplacian by vanishing nonlinearities (in one dimension)
  • Perturbation of the p-Laplacian by vanishing nonlinearities (in one dimension) (en)
skos:notation
  • RIV/49777513:23520/12:43914796!RIV13-MSM-23520___
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  • 8
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  • 158361
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  • RIV/49777513:23520/12:43914796
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  • Asymptotic expansion for large solutions; Prüfer's transformation; Vanishing nonlinearity; Problem at resonance; p-Laplacian; Fredholm alternative (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [217FC25E3DFF]
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  • Nonlinear Analysis
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  • 75
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  • Benedikt, Jiří
  • Girg, Petr
  • Takáč, Peter
issn
  • 0362-546X
number of pages
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  • 10.1016/j.na.2012.01.026
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  • 23520
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