2024

Bal, Kaushik; Mishra, Riddhi; Mohanta, Kaushik

In this paper, we show that the existence of a positive weak solution to the equation (−Δg)su=fu−q(x)inΩ, where Ω is a smooth bounded domain in RN, q∈C1(Ω¯¯), and (−Δg)s is the fractional g-Laplacian with g is the antiderivative of a Young function and f in suitable Orlicz space subjected to zero Dirichlet condition. This includes the mixed fractional (p,q)−Laplacian as a special case. The solution so obtained is also shown to be locally Hölder continuous.