MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SCHRÖDINGER EQUATIONS WITH SATURABLE NONLINEARITY

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doi:10.1007/s10473-021-0213-2

摘要： In this paper, we construct sign-changing radial solutions for a class of Schrödinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer $k$ , by using a minimization argument, we first obtain a sign-changing minimizer with $k$ nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda's theorem, that the minimizer is the desired solution.

关键词: Sign-changing solutions, saturable nonlinearity, Nehari manifold, variational methods

Abstract: In this paper, we construct sign-changing radial solutions for a class of Schrödinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer $k$ , by using a minimization argument, we first obtain a sign-changing minimizer with $k$ nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda's theorem, that the minimizer is the desired solution.

Key words: Sign-changing solutions, saturable nonlinearity, Nehari manifold, variational methods

中图分类号:

35J61

刘忠原. MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SCHRÖDINGER EQUATIONS WITH SATURABLE NONLINEARITY[J]. 数学物理学报(英文版), 2021, 41(2): 493-504.

Zhongyuan LIU. MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SCHRÖDINGER EQUATIONS WITH SATURABLE NONLINEARITY[J]. Acta mathematica scientia,Series B, 2021, 41(2): 493-504.

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