scholarly journals Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dionicio Pastor Dallos Santos
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Nonlinear Boundary Value Problems

We study the existence of solutions for nonlinear boundary value problemsφu′′=ft,u,u′,  lu,u′=0, wherel(u,u′)=0denotes the boundary conditions on a compact interval0,T,φis a homeomorphism such thatφ(0)=0, andf:0,T×R×R→Ris a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.

scholarly journals Lower and Upper Solutions for Even Order Boundary Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 878
Author(s):  
Alberto Cabada ◽  
Lucía López-Somoza
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Existence Of Solution ◽  
Lower And Upper Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Even Order

In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions.

Singular boundary value problems for P-Laplacian-like equations

1997 ◽  
Vol 127 (5) ◽  
pp. 975-981 ◽  
Author(s):  
D. D. Hai ◽  
Seth F. Oppenheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions

SynopsisWe consider the existence of positive solutions to a class of singular nonlinear boundary value problems for P-Laplacian-like equations. Our approach is based on the Schauder Fixed-Point Theorem.

scholarly journals Existence results for nonlinear boundary value problems

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 609-618 ◽  
Author(s):  
Abdeljabbar Ghanmi ◽  
Samah Horrigue
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Nonlinear Boundary Value Problems ◽  
Krasnoselskii Fixed Point Theorem

In the present paper, we are concerned to prove under some hypothesis the existence of fixed points of the operator L defined on C(I) by Lu(t) = ?w0 G(t,s)h(s) f(u(s))ds, t ? I, ? ? {1,?}, where the functions f ? C([0,?); [0,?)), h ? C(I; [0,?)), G ? C(I x I) and (I = [0,1]; if ? = 1, I = [0,?), if ? = 1. By using Guo Krasnoselskii fixed point theorem, we establish the existence of at least one fixed point of the operator L.

scholarly journals The Application of Distributional Henstock-Kurzweil Integral on Third-order Three-Point Nonlinear Boundary-Value Problems

2015 ◽  
Vol 7 (4) ◽  
pp. 150
Author(s):  
Dakai Zhou ◽  
Guoju Ye ◽  
Wei Liu ◽  
Bing Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Nonlinear Boundary Value

We consider a type of form such as $u'''=-f$ with three-point<br />nonlinear boundary-value problems (NBVPs). We verified the existence<br />of solutions of the (NBVPs) when $f$ is distributional<br />Henstock-Kurzweil integral but not Henstock-Kurzweil integral.We use<br />the distribution derivative and fixed point theorem to deal with the<br />problem. The results obtained generalize the known results. For<br />this reason, it is conducive to the further study of NBVPS.

scholarly journals Modification of Lesnic’s Approach and New Analytic Solutions for Some Nonlinear Second-Order Boundary Value Problems with Dirichlet Boundary Conditions

2010 ◽  
Vol 65 (8-9) ◽  
pp. 692-696
Author(s):  
Abdelhalim Ebaid
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Analytic Solutions ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Troesch’S Problem

For solving nonlinear boundary value problems (BVPs), a main difficulty of using Adomian’s method is to find a canonical form which takes into account all the boundary conditions of the problem. This difficulty is overcome by using a modification for Lesnic’s approach developed in this paper. The effectiveness of the proposed procedure is verified by two nonlinear problems: the nonlinear oscillator equation and Troesch’s problem

POSITIVE SOLUTIONS FOR SYSTEMS OF M‐POINT NONLINEAR BOUNDARY VALUE PROBLEMS

2008 ◽  
Vol 13 (3) ◽  
pp. 357-370 ◽  
Author(s):  
Johnny Henderson ◽  
Sotiris K. Ntouyas ◽  
Ioannis K. Purnaras
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Positive solutions (u(t), v(t)) are sought for the nonlocal (m‐point) nonlinear system of boundary value problems, u” + λa(t)f(v) = 0, v” + λb(t)g(u) = 0, for 0 < t < 1, and satisfying, u(0) = 0, u(1) = . An application of a Guo‐Krasnosel'skii fixed point theorem yields sufficient values of λ for which such positive solutions exist.

Two point fractional boundary value problems with a fractional boundary condition

2018 ◽  
Vol 21 (2) ◽  
pp. 442-461 ◽  
Author(s):  
Jeffrey W. Lyons ◽  
Jeffrey T. Neugebauer
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

Abstract In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

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