Three solutions for a Dirichlet boundary value problem involving the -Laplacian

Existence and multiplicity results for elliptic problems with Nonlinear Boundary Conditions and variable exponents

“…Ricceri's three critical points theorem is a powerful tool to study boundary problem of differential equation (see, for example, [1,3,4,5]). Particularly, Mihailescu [17] use three critical points theorem of Ricceri [19] study a particular p(x)-Laplacian equation.…”

Existence of three solutions for p-biharmonic equation

“…In recent years, the three critical points theorem of B. Ricceri has been widely used to solve differential equations, see [1,2,3,5,6,7,9,12,13] and reference therein.…”

“…Our theorem, under the new assumptions, ensures the existence of an open interval Λ ⊆ [0, +∞) and a positive real number ρ such that, for each λ ∈ Λ, problem (P) admits at least three weak solutions whose norms in X are less than ρ. Now, for every x 0 ∈ Ω and selected r 1 , r 2 with r 2 > r 1 > 0, such that B(x 0 , r 1 ) ⊂ B(x 0 , r 2 ) ⊆ Ω, where B(x 0 , r 1 ) denotes the ball with the center at x 0 and radius of r 1 . Put…”

Nontrivial Solutions for Dirichlet Boundary Value Systems with the(p1,…,pn)-Laplacian

“…Due to importance of second-order Dirichlet and Neumann problems in describing a large class of physic phenomena, many authors have studied the existence and multiplicity of solutions for such a problem; we refer the reader to [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein. Some authors also study the system case; see [14][15][16][17][18][19][20].…”