For N ≥ 3 we study the following semipositone problem (Formula Presented) where ∆γ is the Grushin operator (Formula Presented) is a positive function, a > 0 is a parameter and fa is a continuous function on R that coincides with f(t) − a for t ∈ R+, where f is a continuous function with subcritical and Ambrosetti–Rabinowitz type growth and which satisfies f(0) = 0. Depending on the range of a, we obtain the existence of mountain pass solutions in a suitable Sobolev space associated to the Grushin operator, extending the results found in [5] to the Grushin operator.
Mountain pass solutions for an entire semipositone problem involving the Grushin subelliptic operator
Malanchini, Paolo;
2026-01-01
Abstract
For N ≥ 3 we study the following semipositone problem (Formula Presented) where ∆γ is the Grushin operator (Formula Presented) is a positive function, a > 0 is a parameter and fa is a continuous function on R that coincides with f(t) − a for t ∈ R+, where f is a continuous function with subcritical and Ambrosetti–Rabinowitz type growth and which satisfies f(0) = 0. Depending on the range of a, we obtain the existence of mountain pass solutions in a suitable Sobolev space associated to the Grushin operator, extending the results found in [5] to the Grushin operator.File in questo prodotto:
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