Sharp estimates of solutions to the Robin boundary value problem for elliptic non divergence second order equations in a neighborhood of the conical point

2006 ◽  
pp. 407-495
Author(s):  
Mikhail Borsuk
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Conical Point ◽  
Estimates Of Solutions ◽  
Sharp Estimates ◽  
Robin Boundary ◽  
Second Order Equations ◽  
Robin Boundary Value Problem

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 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 Iterative method for solving the second boundary value problem (BVP) for Biharmonic type equation

2016 ◽  
Vol 14 (4) ◽  
pp. 66-72
Author(s):  
Đặng Quang Á
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Second Order ◽  
Second Order Equations

Solving BVPs for the fourth order differential equations by the reduction of them to BVPs for the  second order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by  ourselves in recent works, we construct iterative method for the second BVP for  biharmonic type equation. The convergence rate of  the method is established.

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