The existence of positive solutions for some nonlinear boundary value problems with linear mixed boundary conditions

Abstract

In this paper we study the existence of positive solutions of the equationwhere ϕ : R → R is an increasing homeomorphism and homomorphism and ϕ(0) = 0, subject to linear mixed boundary conditions by a simple application of a fixed point index theorem in cones.

Existence and Iteration of Positive Solutions for One-Dimensional p-Laplacian Boundary Value Problems with Dependence on the First-Order Derivative

“…where a 1 , a 2 ≥ 0 and φ is an increasing positive homomorphism and homeomorphism with φ 0 0 for more details, see [11][12][13] . In that paper, the authors claimed that u ∈ C 0, 1 ∩ …”

Existence of Three Positive Solutions of Three-Order with m-Point Impulsive Boundary Value Problems

“…However in this paper we define a new operator which improves and generates a p-Laplacian operator for some p > 1 and ϕ is not necessarity odd. Moreover for increasing homeomorphism and positive homomorphism operator and research has proceeded very slowly, see [10,11]. Especially the existence of three positive solutions for three-order with m-point impulsive boundary value problems still remains unknown.…”

“…In [11], Liu and Zhang studied the existence of positive solutions of quasi-linear differential equation…”

“…Motivated by papers [5,11,13], we prove in this work the existence of three positive solutions to (1) and (2) which have specific scope. The arguments developed in this paper are five functionals fixed-point theorem [3] and our main result extends the study made in [3], So the goal of the present paper is to improve and generate p-Laplacian operator and establish some criteria for the existence of three positive solutions by means of five functionals fixed-point theorem.…”

Existence of positive solutions for nonlinear singular boundary value problem with p -Laplacian

“…In paper [14], Liu studied the existence of positive solutions of quasilinear differential equation ((x )) +a(t)f (x(t)) = 0, t∈ (0, 1)…”