On the Continuation Poincaré Method and Its Application to the Multi-valued Boundary Value Problems |
Contents
Existence theorems for multivalued boundary value problems | 2 |
On the continuation Poincare method | 8 |
Example | 20 |
3 other sections not shown
Common terms and phrases
a.e. on G absolutely continuous functions admissible boundary value admissible couple Arzela-Ascoli theorem Banach space Bo n Ker Bonker boundary value problem bounded set Caratheodory conditions center in zero closed subspace comp completely continuous mapping convex set convex-valued mapping given convex-valued mapping satisfying couple of problem d(Ny Darboux problem denote E₂ EnKer exists a ball exists at least fact is obvious following boundary value following condition following existence theorem following fact formula 1.5 given by formula K₁-admissible couple L_(G l₁ l₁(X l₂ least one solution linear mapping mapping and let mapping E,Y mapping F Multi-valued boundary value multi-valued mapping open set ordinary differential equations partial differential equations problem 1.1 problem II proof is completed Proposition real number right inverse satisfies assumption 4.2.1 satisfies Condition C₁ satisfying conditions 5.1 satisfying the Caratheodory single-valued mapping solution of problem supess f