Abstract
In this work, we study the existence and the multiplicity of non-negative solutions for the following problem
(P-lambda) {Lu = a(x)u(q) + lambda b(x)u(p) in Omega,
u = 0, in R-n\Omega,
where Omega subset of R-n (n >= 2), is a bounded smooth domain, lambda, p, q are positive real numbers, s is an element of (0, 1), a, b are continuous functions, and L is a nonlocal operator defined later by (1.1). We establish the existence and we give amultiplicity of solutions by constrained minimization of the Euler-Lagrange functional corresponding to the problem (P-lambda), on suitable subsets of Nehari manifold and using the fibering maps. Precisely, we show the existence of lambda(0) > 0, such that for all lambda is an element of (0, lambda(0)), problem (P-lambda) has at least two non-negative solutions.