Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

Positive solutions for one-dimensional p-Laplacian boundary value problems with nonlinear parameter

In this paper, we establish existence of positive solutions of the nonlinear problems of one dimensional p-Laplacian with nonlinear parameter φp(u ′(t))′ + a(t)f(λ, u) = 0, t ∈ (0, 1), u(0) = u(1) = 0. where a : Ω→ R is continuous and may change sign, λ > 0 is a parameter, f(λ, 0) > 0 for all λ > 0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.

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

EXISTENCE OF POSITIVE PSEUDO-SYMMETRIC SOLUTIONS FOR ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY-VALUE PROBLEMS

We prove the existence of positive pseudo-symmetric solutions for four-point boundary-value problems with p-Laplacian. Also we present an monotone iterative scheme for approximating the solution. The interesting point here is that the nonlinear term f involves the first-order derivative.

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 ...

Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One - Dimensional p 1 , . . . , pn - Laplacian Operator

and Applied Analysis 3 Here and in the sequel, X will denote the Cartesian product of n space Xi ⎧ ⎨ ⎩ ξ ∈ W1,pi 0, 1 ; ξ 0 m ∑ j 1 ajξ ( xj ) , ξ 1 m ∑ j 1 bjξ ( xj ) ⎫ ⎬ ⎭ , 1.6 for i 1, . . . , n, that is, X X1 × · · · ×Xn equipped with the norm ‖ u1, . . . , un ‖ n ∑ i 1 ∥ ∥ui ∥ ∥ pi , 1.7