Approximate radial symmetry for solutions of a class of boundary value problems in ring-shaped domains

This paper deals with some classical boundary value problems defined in the ring-shaped region $\Omega \backslash\overline{B(R_0)} \subset \Bbb{R}^N$, where B(R ₀) is the N-ball of radius R ₀ centered at the origin and contained in . The authors investigate how the geometry of is affected by some overdertermined data. In particular they show that must be nearly spherical if the overdetermined data are nearly constants.     

Transparent boundary conditions for a class of boundary value problems in some ramified domains with a fractal boundary

We consider some boundary value problems in self-similar ramified domains, with Laplace and Helmholtz equations. We discuss transparent boundary conditions. These conditions permit computing the restriction of the solutions to domains obtained by stopping the geometric construction after a finite number of steps. To cite this article: Y. Achdou et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Existence of solutions for a class of third-order nonlinear boundary value problems

In this paper, we are concerned with the following third-order ordinary differential equation:

     

Positive solutions for a class of boundary value problems on infinite intervals

This paper studies the existence of nonegative solutions to the two point boundary value , 0<t< with appropriate boundary conditions.     

Infinitely many solutions for a class of discrete non-linear boundary value problems

The existence of infinitely many solutions for a discrete non-linear Dirichlet problem involving the p-Laplacian, under appropriate oscillating behaviours of the non-linear term, is established. The approach is based on the critical point theory.     

Uniqueness of solutions of boundary value problems in unbounded domains for parabolic equations

The dependence of the uniqueness classes of the solutions of boundary value problems for second-order parabolic equations on the coefficients of the equation and on the geometry of an unbounded domain is investigated.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 123–136, 1988.     

Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.