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Nonlocal carrier’s double phase problem
Published online by Cambridge University Press: 13 November 2025
Abstract
We study the existence and multiplicity of positive bounded solutions for a class of nonlocal, non-variational elliptic problems governed by a nonhomogeneous operator with unbalanced growth, specifically the double phase operator. To tackle these challenges, we employ a combination of analytical techniques, including the sub-super solution method, variational and truncation approaches, and set-valued analysis. Furthermore, we examine a one-dimensional fixed-point problem.To the best of our knowledge, this is the first workaddressing nonlocal double phase problems using these methods.
MSC classification
Primary:
35A01: Existence problems
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- Research Article
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- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
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