Positive solutions of nonhomogeneous boundary value problems for some nonlinear equation with ϕ-LaplacianReport as inadecuate




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Boundary Value Problems

, 2012:130

Jean Mawhin-s Achievements in Nonlinear Analysis

Abstract

We will consider the nonhomogeneous ϕ-Laplacian differential equation

{ ϕ u ′ t ′ = − h t f u t , t ∈ 0 , T , u 0 = ∑ i = 1 k α i u η i , ϕ u ′ T = β , Open image in new windowwhere ϕ : R → − b , b Open image in new window 0 < b ≤ + ∞ Open image in new window is an increasing homeomorphism such that ϕ 0 = 0 Open image in new window, h : 0 , T → R + Open image in new window and f : R + → R + Open image in new window are continuous, β ≥ 0 Open image in new window and η i ∈ 0 , T Open image in new window and α i ∈ R Open image in new window, i = 1 , 2 , … , k Open image in new window. Based on the Krasnosel’skii fixed point theorem, the existence of a positive solution is obtained, even if some of the α i Open image in new window coefficients are negative. Two examples are also given to illustrate our main results.

Keywordsnonhomogeneous ϕ-Laplacian positive solution fixed point negative coefficient  Download fulltext PDF



Author: Liang-Gen Hu - Jing Xu

Source: https://link.springer.com/



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