TY - JOUR
T1 - Quasilinear Fractional Neumann Problems
AU - Mugnai, Dimitri
AU - Lippi, Edoardo Proietti
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed.
AB - We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed.
KW - mixed local and fractional p-Laplacians
KW - Neumann boundary conditions
KW - regularity
KW - superlinear problems
UR - http://www.scopus.com/inward/record.url?scp=85214525167&partnerID=8YFLogxK
U2 - 10.3390/math13010085
DO - 10.3390/math13010085
M3 - Article
AN - SCOPUS:85214525167
SN - 2227-7390
VL - 13
JO - Mathematics
JF - Mathematics
IS - 1
M1 - 85
ER -