Solution of the first biharmonic problem by the method of least squares on the boundary
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I
Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation
Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.
Solvability of nonlinear problems at resonance
Solvability of the superlinear elliptic boundary value problem
Solving the multidimensional difference biharmonic equation by the Monte Carlo method.
Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations
This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in , on ∂Ω in the Sobolev space , where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.
Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem
The numerical solution of the model fourth-order elliptic boundary value problem in two dimensions is presented. The iterative procedure in which the biharmonic operator is splitted into two Laplace operators is used. After formulating the finite-difference approximation of the procedure, a formula for the evaluation of the transformed iteration vectors is developed. The Jacobi semi-iterative, Richardson and A.D.I. iterative Poisson solvers are applied to compute one transformed iteration vector....
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities.
Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions
The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples....
Spikes in two coupled nonlinear Schrödinger equations
Strong ellipticity of boundary integral operators.
Strongly elliptic linear operators without coercive quadratic forms I. Constant coefficient operators and forms
A family of linear homogeneous 4th order elliptic differential operators with real constant coefficients, and bounded nonsmooth convex domains are constructed in so that the have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces .
Strongly nonlinear elliptic boundary value problems
Sul problema di Dirichlet in un cono per l’equazione
Sulla regolarita delle soluzioni di equazioni ellittiche negli spazi
Sur la convergence des schémas aux différences finies pour des équations elliptiques du quatrième ordre avec des solutions irrégulières. (Convergence of finite difference schemes for fourth order elliptic equations with irregular solutions).
Sur la solution d'un problème de la plaque
Sur le problème de Dirichlet pour l'équation aux dérivées partielles du quatrième ordre du type elliptique