A result on elliptic systems with Neumann conditions via Ricceri’s three critical points theorem

Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

“…If we take f (x,t) = |t| g(x)-2 t -t with γ (x) ∈ C 0 (¯ ) satisfies 2 <g -≤ g + <p -, μ = 0, Corollary 1 becomes a version of Theorem 2 in [23]. Hence our Corollary 1 unifies and generalizes Theorem 2 in [21] and Theorem 2 in [23] and our Theorem 2 generalizes the main results of [21][22][23][24][25] to the system (1). At last, we give two examples.…”

“…Li and Tang in [24] obtained the existence of at least three weak solutions to problem (1) when p(x) ≡ p with Dirichlet boundary value conditions. El Manouni and Kbiri Alaoui [25] obtained the existence of at least three solutions of system (1) when p(x) ≡ p in Ω by the three critical points theorem obtained by Ricceri [26].…”

EXISTENCE OF THREE SOLUTIONS FOR A CLASS OF NAVIER QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE (p1, …, pn)-BIHARMONIC

“…In recent years, the three critical points theorem of B. Ricceri has been widely used to solve differential equations (see [2,4,6,8,10,13,14,15,21,23] and references therein). Using the three critical points theorem, some authors have considered the elliptic systems.…”

“…Afrouzi and Heidarkhani [1] unify and generalize Li and Tang's problem. In [8], El Manouni and Kbiri Alaoui consider (p, q)-Laplacian systems with Neumann conditions via Ricceri's three critical points theorem. Li and Tang [14] consider a (p, q)-biharmonic system under Navier boundary condition.…”

Multiple Solutions for Gradient Elliptic Systems with Nonsmooth Boundary Conditions

“…Three critical points theorems of B. Ricceri [11], [12], [14] were the starting point for recent investigations of the existence of multiple solutions for different classes of quasilinear elliptic systems involving the (p, q)-Laplacian, for example the papers of J. Liu, X. Shi [7], C. Li, C.-L. Tang [6] (with homogeneous Dirichlet boundary conditions), as well as of G. Dai [2] (on the whole space R N ), S. E. Manouni, M. K. Alaoui [9] (with homogeneous Neumann boundary conditions).…”