Existence and uniqueness of a positive solution to double phase problems involving discontinuous Kirchhoff type functions
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This paper is devoted to establishing the existence of a unique positive weak solution to double phase problems with discontinuous Kirchhoff coefficients. The main tools are the uniqueness result of Br\'{e}zis-Oswald type problem and the abstract global minimum principle of Ricceri. In particular, we employ the inequality of D\`{i}az-Saa type to observe the existence of a unique positive weak solution to a nonlinear problem of Br\'{e}zis-Oswald type involving the double phase operator.
Abstract
This paper is devoted to establishing the existence of a unique positive weak solution to double phase problems with discontinuous Kirchhoff coefficients. The main tools are the uniqueness result of Br\'{e}zis-Oswald type problem and the abstract global minimum principle of Ricceri. In particular, we employ the inequality of D\`{i}az-Saa type to observe the existence of a unique positive weak solution to a nonlinear problem of Br\'{e}zis-Oswald type involving the double phase operator.