scholarly journals Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

2017 ◽  
Vol 15 (1) ◽  
pp. 1549-1557 ◽  
Author(s):  
Yuhua Long ◽  
Baoling Zeng
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Parameter Dependence ◽  
Invariant Sets ◽  
Sign Changing Solutions ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

Abstract In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

scholarly journals Infinitely Many Solutions for a Robin Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-9
Author(s):  
Aixia Qian ◽  
Chong Li
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Boundary Value ◽  
Elliptic Problems ◽  
Infinitely Many Solutions ◽  
Weaker Conditions ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

By combining the embedding arguments and the variational methods, we obtain infinitely many solutions for a class of superlinear elliptic problems with the Robin boundary value under weaker conditions.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
I. Ibrango ◽  
S. Ouaro
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Boundary Value ◽  
Monotone Operators ◽  
Robin Boundary Conditions ◽  
Anisotropic Problems ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak solutions converges to a measurable function which is the entropy solution of the anisotropic Robin boundary value problem.

scholarly journals Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yansheng He ◽  
Mingzhe Sun ◽  
Chengmin Hou
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Value Problem ◽  
Multiple Positive Solutions ◽  
Order Difference ◽  
Nonlinear Boundary Value ◽  
Order Difference Equation

We consider a discrete fractional nonlinear boundary value problem in which nonlinear termfis involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

scholarly journals POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

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