On a class of nonlinear variational inequalities: high concentration of the graph of weak solution via its fractional dimension and Minkowski content.
We discuss an open question of Kiguradze and Chanturia about Property and Property for the equation . The proposed integral criterion is proved in a few cases.
A class of functional boundary conditions for the second order functional differential equation is introduced. Here is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.
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.