Weak solutions for nonlocal problems in fractional Orlicz-Sobolev spaces
Keywords:
Fractional order Sobole spaces, nonlocal problems, weak solutions, critical points.Abstract
We study a class of nonlocal boundary value problems involving the fractional a(·)-Laplacian operator in fractional Orlicz–Sobolev spaces.The main equation features nonlinear source terms with a nonnegative parameterμand is posed on a bounded domain with homogeneous Dirichlet conditions in the nonlocal sense. Using variational approaches, we establish the existence of at least one nontrivial, non negative weak solution when the parameter μ is sufficiently small. Furthermore, we identify conditions under which the solution is strictly positive. Two examples are included to demonstrate the applicability of the main result
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