In this paper, we establish the existence of at least three solutions of the multi-point boundary value system ⎧ ⎨ ⎩ −(φp i (u i)) = λFu i (x, u1,. .. , un), t ∈ (0, 1), ui(0) = m j=1 ajui(xj), ui(1) = m j=1 bjui(xj), The approaches used are based on variational methods and critical point theory.
The existence of three distinct weak solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian operator is established under suitable assumptions on the nonlinear term. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces.
The existence of a non-trivial solution for a discrete non-linear Dirichlet problem involving p-Laplacian is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Bonanno. Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Existence of three positive… (More)
A critical points approach for the existence of multiple solutions of a Dirichlet quasilinear system, Optimal existence theorems for positive solutions of second order multi-point boundary value problems, Commun. Positive solutions for a semipositone fractional boundary value problem with a forcing term, Fract. Positive solutions of nonlinear fractional… (More)
Applying two three critical points theorems, we prove the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion with a perturbed nonlinearity and two parameters.