A Variational Approach for One-Dimensional Scalar Field Problems

Armin Hadjian ()
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Armin Hadjian: University of Bojnord

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 4, 621-632

Abstract: Abstract In this paper, we are interested in the existence of infinitely many weak solutions for a onedimensional scalar field problem. By using variational methods, in an appropriate functional space which involves the potential V, we determine intervals of parameters such that our problem admits either a sequence of weak solutions strongly converging to zero provided that the nonlinearity has a suitable behavior at zero or an unbounded sequence of weak solutions if a similar behavior occurs at infinity.

Keywords: One-dimensional scalar field problem; variational methods; infinitely many solutions (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0290-7

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