Positive Solutions for Discrete Boundary Value Problems to One-Dimensionalp-Laplacian with Delay

Positive Solutions for Discrete Boundary Value Problems to One-Dimensional p-Laplacian with Delay

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...

Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian

We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ φp Δu t − 1 q t f t, u t ,Δu t 0, t ∈ {1, . . . , n − 1} subject to the boundary conditions: u 0 0, u n ∑m−2 i 1 aiu ξi , where φp s |s|p−2s, p > 1, ξi ∈ {2, . . . , n − 2} with 1 < ξ1 < · · · < ξm−2 < n − 1 and ai ∈ 0, 1 , 0 < ∑m−2 i 1 ai < 1. Using a new fixed point theorem due to Avery and...

Positive solutions for nonlinear systems of third-order generalized sturm-liouville boundary value problems with $(p_1,p_2,ldots,p_n)$-laplacian

In this work, byemploying the Leggett-Williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-Laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

Existence of positive solutions for discrete delta-nabla fractional boundary value problems with p-Laplacian

where t ∈ T = [ν – β – 1,b + ν – β – 1]Nν–β–1 . βν–2, b∇ν are left and right fractional difference operators, respectively, and φp(s) = |s|p–2s, p > 1. By using the method of upper and lower solution and the Schauder fixed point theorem, we obtain the existence of positive solutions for the above boundary value problem; and applying a monotone iterative technique, we establish iterative schemes...