ON KIRCHHOFF-HARDY TYPE PROBLEMS INVOLVING DOUBLE PHASE OPERATORS

doi:10.1007/s10473-025-0504-0

摘要/Abstract

摘要： This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials. The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential, the absence of the compactness condition of Palais-Smale, and the $L^{\infty}$-bound for any possible weak solution. To establish multiplicity results, we utilize the fountain theorem and the dual fountain theorem as main tools. Also, we give the $L^{\infty}$-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique. As an application, we give the existence of a sequence of infinitely many weak solutions converging to zero in $L^{\infty}$-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.

关键词: double phase problems, Musielak-Orlicz-Sobolev spaces, variational methods, multiple solutions, De Giorgi iteration method

Abstract: This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials. The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential, the absence of the compactness condition of Palais-Smale, and the $L^{\infty}$-bound for any possible weak solution. To establish multiplicity results, we utilize the fountain theorem and the dual fountain theorem as main tools. Also, we give the $L^{\infty}$-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique. As an application, we give the existence of a sequence of infinitely many weak solutions converging to zero in $L^{\infty}$-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.

Key words: double phase problems, Musielak-Orlicz-Sobolev spaces, variational methods, multiple solutions, De Giorgi iteration method

中图分类号:

35B38

Yun-Ho KIM, Taek-Jun JEONG, Jun-Yeob, SHIM. ON KIRCHHOFF-HARDY TYPE PROBLEMS INVOLVING DOUBLE PHASE OPERATORS[J]. 数学物理学报(英文版), 2025, 45(5): 1814-1854.

Yun-Ho KIM, Taek-Jun JEONG, Jun-Yeob, SHIM. ON KIRCHHOFF-HARDY TYPE PROBLEMS INVOLVING DOUBLE PHASE OPERATORS[J]. Acta mathematica scientia,Series B, 2025, 45(5): 1814-1854.

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