We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on exterior bounded domain. prove existence positive weak solution for classes nonlinearities which are either sublinear or asymptotically linear at infinity. use method sub-and-supersolutions to establish results. also provide numerical bifurcation diagrams, corresponding theoretical r...

We prove the existence of ground state solutions to critical growth p-Laplacian and fractional problems that are nonresonant at zero.

In this article, we prove the existence of multiple solutions for following fractional Schrödinger-Poisson system with sign-changing potential (−∆)u+ V (x)u+ λφu = f(x, u), x ∈ R, (−∆)φ = u, x ∈ R, where (−∆)α denotes the fractional Laplacian of order α ∈ (0, 1), and the potential V is allowed to be sign-changing. Under certain assumptions on f , we obtain infinitely many solutions for this sys...

In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on ...