On a class of nonlinear variational inequalities: high concentration of the graph of weak solution via its fractional dimension and Minkowski content.
The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.
Existence and uniqueness of the solution to a fourth order nonlinear vector periodic boundary value problem is proved by using the estimates for derivatives of the Green function for the corresponding homogenous scalar problem
A criterion for the unique solvability of and sufficient conditions for the correctness of the modified Vallèe-Poussin problem are established for the linear ordinary differential equations with singularities.
We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.