scholarly journals Solvability for p-Laplacian boundary value problem at resonance on the half-line

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Weihua Jiang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Half Line ◽  
At Resonance ◽  
Problem At Resonance

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

scholarly journals Existence theorems for a second orderm-point boundary value problem at resonance

1995 ◽  
Vol 18 (4) ◽  
pp. 705-710 ◽  
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Theorems ◽  
Boundary Value ◽  
Continuation Theorem ◽  
Point Boundary ◽  
Existence Of A Solution ◽  
At Resonance ◽  
Problem At Resonance

Letf:[0,1]×R2→Rbe function satisfying Caratheodory's conditions ande(t)∈L1[0,1]. Letη∈(0,1),ξi∈(0,1),ai≥0,i=1,2,…,m−2, with∑i=1m−2ai=1,0<ξ1<ξ2<…<ξm−2<1be given. This paper is concerned with the problem of existence of a solution for the following boundary value problemsx″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=x(η),x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=∑i=1m−2aix(ξi).Conditions for the existence of a solution for the above boundary value problems are given using Leray Schauder Continuation theorem.

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