Analysis reveals multiple solutions in elliptic equations with logarithmic double phase operators, suggesting potential applications in mathematical modeling.
In this paper, we study elliptic equations of the form where is the logarithmic double phase operator given by is Euler's number, , , is a bounded domain with Lipschitz boundary , , with , and . Under mild assumptions on the nonlinearity we prove multiplicity results for the problem above and get two constant sign solutions and another third nontrivial solution. This third solution is obtained by using the theory of critical groups. As a result of independent interest, we show that every weak solution of the problem above is essentially bounded.
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Rădulescu et al. (2025) studied this question.
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