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 work addressing nonlocal double phase problems using these methods.
Nonlocal carrier’s double phase problem
Failla, Giuseppe
;
2025-01-01
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 work addressing nonlocal double phase problems using these methods.File in questo prodotto:
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