This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose $W_{0}^{1,H}(\varOmega )$ -norms and $L^{\infty }$ -norms tend to zero under suitable hypotheses about nonlinearity.

中文翻译：

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双相问题的无限多个正解

本文涉及一类双相问题的无限多个正解的存在。通过变分方法和Musielak-Orlicz-Sobolev空间的理论，我们建立了无限多个正解的存在，这些正解的存在$ W_ {0} ^ {1，H}（\ varOmega）$-范数和$ L ^ {\ infty } $-范数在有关非线性的适当假设下趋于零。