Shapour Heidarkhani

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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.
where pi > 1 and φpi(t) = |t|pi−2t for i = 1, . . . , n, λ is a positive parameter, m, n ≥ 1 are integers, aj , bj ∈ R for j = 1, . . . ,m, and 0 < x1 < x2 < x3 < . . . < xm < 1. Here, F : [0, 1] × R → R is a function such that the mapping (t1, t2, . . . , tn) → F (x, t1, t2, . . . , tn) is in C in R for all x ∈ [0, 1], Fti is continuous in [0, 1]× R for i(More)