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An Evolutionary Boundary Value Problem
Mediterranean Journal of Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aissa Benseghir, Mircea Sofonea
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On a Multidimensional Boundary Value Problem
Differential Equations, 2005The author considers the existence of a solution for a nonlinear boundary value problem of the form \[ \ddot z_j+ \sum^m_{i=1} b_{ij}(z)\dot z_i\dot z_j= 0,\quad z_j(0)= 0,\quad z_j(1)= 1,\quad j= 1,\dots, m, \] with the additional condition \(0\leq z_j(s)\leq 1\), \(0\leq s\leq 1\), \(j= 1,\dots, m\), where the \(b_{ij}(z)\) are smooth scalar ...
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Boundary-value problems with nonlinear boundary conditions
Nonlinearity, 1988The authors deal with a general boundary value problem of the type: \(x'=F(t,x),T(x)=y,y\in R^ n\) where \(F(t,x)=A(t)x+f(t,x)\) and T is a continuous but not necessarily linear operator. It is shown that under suitable conditions the problem has at least one solution. The proof relies on a fixed-point theorem for condensing maps.
ANICHINI, GIUSEPPE, CONTI, GIUSEPPE
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Elementary Boundary Value Problems
American Journal of Physics, 1966The solution of a particular elementary boundary value problem is presented. A new set of orthogonal functions is needed. Their properties are discussed briefly. A comment is made about the number of independent solutions of a rth order equation in an n dimensional space. The number is rn and not r·n.
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2011
This chapter deals with Newton methods for boundary value problems (BVPs) in nonlinear partial differential equations (PDEs). There are two principal approaches: (a) finite dimensional Newton methods applied to given systems of already discretized PDEs, also called discrete Newton methods, and (b) function space oriented inexact Newton methods directly
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This chapter deals with Newton methods for boundary value problems (BVPs) in nonlinear partial differential equations (PDEs). There are two principal approaches: (a) finite dimensional Newton methods applied to given systems of already discretized PDEs, also called discrete Newton methods, and (b) function space oriented inexact Newton methods directly
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General Boundary-Value Problems
1992Section 5.1 introduces the general elliptic linear differential equation of second order together with the Dirichlet boundary values. An important statement is the maximum-minimum principle in §5.1.2. In §5.1.3 sufficient conditions for the uniqueness of the solution and the continuous dependence on the data are proved.
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A multilevel solver for boundary value problems
IEEE Transactions on Electron Devices, 1985Multilevel methods have been studied extensively for solving certain partial differential equations, and such equation solvers have been successfully applied to major computational problems of physical interest and technological importance. KLEV is a collection of routines for solving the N \times N system of linear equations Az = g when A and g are ...
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2014
In this chapter we discuss boundary value problems for second order nonlinear equations. The linear case has been discussed in Chapter 9.
Shair Ahmad, Antonio Ambrosetti
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In this chapter we discuss boundary value problems for second order nonlinear equations. The linear case has been discussed in Chapter 9.
Shair Ahmad, Antonio Ambrosetti
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2012
When solving initial value problems for ordinary differential equations, differential algebraic equations or partial differential equations, as discussed in previous chapters, a unique solution to the equations, if it exists, is obtained by specifying the values of all the components at the starting point of the range of integration.
Karline Soetaert +2 more
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When solving initial value problems for ordinary differential equations, differential algebraic equations or partial differential equations, as discussed in previous chapters, a unique solution to the equations, if it exists, is obtained by specifying the values of all the components at the starting point of the range of integration.
Karline Soetaert +2 more
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A boundary value problem with eigenvalue on the boundary
Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery on - ACM '59, 1959B. A. Troesch +2 more
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