Study of fractional semipositone problems on RN

• Autorzy: Biswas Nirjan

Identyfikatory

DOI

10.7494/OpMath.2024.44.4.445

• Języki publikacji: EN

Abstrakty

EN

Let s ∈ (0, 1) and N > 2s. In this paper, we consider the following class of nonlocal semipositone problems: (−Δ)su = g(x)ƒa(u) in RN, u > 0 in RN, where the weight g ∈ L1(RN) ∩ L∞(RN) is positive, a > 0 is a parameter, and ƒa ∈ C(R) is strictly negative on (−∞, 0]. For ƒa having subcritical growth and weaker Ambrosetti–Rabinowitz type nonlinearity, we prove that the above problem admits a mountain pass solution ua, provided a is near zero. To obtain the positivity of ua, we establish a Brezis–Kato type uniform estimate of (ua) in Lr(RN) for every r ∈ [formula].

Słowa kluczowe

EN

semipositone problems; fractional operator; uniform regularity estimates; positive solutions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 4
• Strony: 445--470
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Biswas Nirjan

• Tata Institute of Fundamental Research, Centre For Applicable Mathematics, Post Bag No. 6503, Sharada Nagar, Bangalore 560065, India

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)