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A differentiable variational model for structural self-contact and fracture. [PDF]

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Boundary-value problems with nonlinear boundary conditions

Nonlinearity, 1988
The 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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Some Nonlinear Boundary Value Problems

SIAM Journal on Mathematical Analysis, 1976
Let $\Omega \subset R^m $ be a bounded domain and ${\bf L}$ a second order uniformly strongly elliptic partial differential operator. Let ${\bf B}$ be a linear boundary operator. Suppose $f(x,u)$ and $g(x,u)$ are functions on $\Omega \times R^1 $ which are nonincreasing with respect to u for sufficiently large values of $| u |$.
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Degenerate nonlinear boundary-value problems

Ukrainian Mathematical Journal, 2009
We establish necessary and sufficient conditions for the existence of solutions of weakly nonlinear degenerate boundary-value problems for systems of ordinary differential equations with a Noetherian operator in the linear part. We propose a convergent iterative procedure for finding solutions and establish the relationship between necessary and ...
O. A. Boichuk, L. M. Shehda
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