We study the existence of positive weak solutions for the following problem: where is a bounded domain in with smooth boundary, is a bounded measurable function on , is nonnegative real number, is the unit outer normal to , , and . The functions and have critical exponential growth, while and are their primitives. The proofs combine the constrained minimization method with energy methods and topological tools.
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Rawat et al. (2024) studied this question.
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