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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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1992
The simplest frictionless contact problem of the class defined by equations (29.3–29.6) is that in which the contact area A is the circle 0 < r < a and the indenter is axisymmetric, in which case we have to determine a harmonic function φ(r, z) to satisfy the mixed boundary conditions $$\frac{{\partial \varphi }}{{\partial z}} = - \frac{\mu }{{(1 -
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The simplest frictionless contact problem of the class defined by equations (29.3–29.6) is that in which the contact area A is the circle 0 < r < a and the indenter is axisymmetric, in which case we have to determine a harmonic function φ(r, z) to satisfy the mixed boundary conditions $$\frac{{\partial \varphi }}{{\partial z}} = - \frac{\mu }{{(1 -
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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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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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Geodetic boundary value problems I
1986Veröffentlichungen des Zentralinstituts Physik der Erde ...
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Carleman boundary value problems and boundary value problems of Carleman type
2000If we suppose that limit values of the same unknown function are conjugated in the boundary value conditions (8.2) and (8.3), then we obtain two more binomial boundary value problems with a shift: $$ \Phi ^ + \left( {\alpha _ - \left( t \right)} \right) = G\left( t \right)\Phi ^ + \left( t \right) + g\left( t \right) $$ (I3) , $$ \Phi ^ +
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