Multiplicity of Positive Solutions for Second Order Nonlinear Dirichlet Problem with One-dimension Minkowski-Curvature Operator

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu
Keyword(s):  
Dirichlet Problem ◽  
Positive Solutions ◽  
Second Order ◽  
One Dimension ◽  
Curvature Operator ◽  
Multiple Positive Solutions ◽  
Nonlinear Dirichlet Problem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this work, we study the existence and multiplicity of positive solutions for nonlinear Dirichlet problem with one-dimension Minkowski-curvature operator,where k > 0 is a constant, λ > 0 is a parameter and f : [0,∞) → ℝ is continuous. We apply the quadrature arguments to prove how changes in the sign of f (u) lead to multiple positive solutions of the above problem for sufficiently large λ.

scholarly journals Multiple positive solutions of second-order nonlinear difference equations with discrete singular ϕ-Laplacian

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaoxiao Su ◽  
Ruyun Ma
Keyword(s):  
Dirichlet Problem ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Second Order ◽  
Topological Method ◽  
Multiple Positive Solutions ◽  
Nonlinear Difference Equations ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractWe consider the existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear difference equation $$ \textstyle\begin{cases} -\nabla [\phi (\triangle u(t))]=\lambda a(t,u(t))+\mu b(t,u(t)), \quad t\in \mathbb{T}, \\ u(1)=u(N)=0, \end{cases} $$ { − ∇ [ ϕ ( △ u ( t ) ) ] = λ a ( t , u ( t ) ) + μ b ( t , u ( t ) ) , t ∈ T , u ( 1 ) = u ( N ) = 0 , where $\lambda ,\mu \geq 0$ λ , μ ≥ 0 , $\mathbb{T}=\{2,\ldots ,N-1\}$ T = { 2 , … , N − 1 } with $N>3$ N > 3 , $\phi (s)=s/\sqrt{1-s^{2}}$ ϕ ( s ) = s / 1 − s 2 . The function $f:=\lambda a(t,s)+\mu b(t,s)$ f : = λ a ( t , s ) + μ b ( t , s ) is either sublinear, or superlinear, or sub-superlinear near $s=0$ s = 0 . Applying the topological method, we prove the existence of either one or two, or three positive solutions.

scholarly journals Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

scholarly journals Existence of multiple positive solutions for semipositone fractional boundary value problems

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 749-759 ◽  
Author(s):  
Şerife Ege ◽  
Fatma Topal
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Fractional Boundary Value Problems

In this paper, we study the existence and multiplicity of positive solutions to the four-point boundary value problems of nonlinear semipositone fractional differential equations. Our results extend some recent works in the literature.

scholarly journals Positive Solutions for Second-Order Nonlinear Ordinary Differential Systems with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Lan Sun ◽  
Yukun An ◽  
Min Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Differential Systems ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Two Parameters

By using fixed-point theorem and under suitable conditions, we investigate the existence and multiplicity positive solutions to the following systems: , where are four positive constants and , , and . We derive two explicit intervals of and , such that the existence and multiplicity of positive solutions for the systems is guaranteed.

Multiple positive solutions for a nonlinear Dirichlet problem with non-convex vector-valued response

2005 ◽  
Vol 135 (1) ◽  
pp. 105-117 ◽  
Author(s):  
Andrzej Nowakowski ◽  
Andrzej Rogowski
Keyword(s):  
Dirichlet Problem ◽  
Positive Solutions ◽  
Multiple Positive Solutions ◽  
Nonlinear Dirichlet Problem ◽  
Image Position ◽  
Vector Valued

In this paper we establish the existence of many positive solutions to with Vx a vector-valued nonlinearity.

Multiple positive solutions of elliptic systems in exterior domains

2018 ◽  
Vol 20 (06) ◽  
pp. 1750063 ◽  
Author(s):  
Haidong Liu ◽  
Zhaoli Liu
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Elliptic Systems ◽  
Continuous Functions ◽  
Multiple Positive Solutions ◽  
Exterior Domains ◽  
Existence And Multiplicity ◽  
Large Ball ◽  
Multiplicity Of Positive Solutions ◽  
Positive Functions

In this paper, existence and multiplicity of positive solutions of the elliptic system [Formula: see text] is proved, where [Formula: see text] is an exterior domain in [Formula: see text] such that [Formula: see text] is far away from the origin and contains a sufficiently large ball, [Formula: see text], and the coefficients [Formula: see text] are continuous functions on [Formula: see text] which tend to positive constants at infinity. We do not assume [Formula: see text] to be positive functions.

scholarly journals Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Tsing-San Hsu
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equation ◽  
Nehari Manifold ◽  
Weight Functions ◽  
Multiple Positive Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
The Nehari Manifold

Existence and multiplicity of positive solutions for the following semilinear elliptic equation: in , , are established, where if if , , satisfy suitable conditions, and maybe changes sign in . The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold.

scholarly journals The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Fuli Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Point Index ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

The existence and multiplicity of positive solutions are established for second-order periodic boundary value problem. Our results are based on the theory of a fixed point index for A-proper semilinear operators defined on cones due to Cremins. Our approach is different in essence from other papers and the main results of this paper are also new.

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