M. Aitalioubrahim
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Existence of solutions for lower semi-continuous non-convex differential inclusions with $\phi-$Laplacian
Najib Askouraye, Myelkebir Aitalioubrahim
MFAT 32 (2026), no. 1, 25-34
25-34
We show the existence of solutions satisfying Cauchy or terminal boundary conditions for first order differential inclusion $(\phi(x(t)))'\in F(t,x(t))$. We consider the second order problem $(\phi(x'(t)))'\in F(t,x(t))$ with many boundary conditions. The set-valued map $F$ has non-convex values and the function $\phi$ satisfies a weak condition. The resolution method use the topological degree without the method of upper and lower solutions.
Viability result for higher-order functional differential inclusions
MFAT 26 (2020), no. 3, 189-200
189-200
We prove, in separable Banach spaces, the existence of viable
solutions for the following higher-order functional differential
inclusion
$$
x^{(k)}(t) \in
F(t,T(t)x,x^{(1)}(t),...,x^{(k-1)}(t)),\quad\mbox{a.e. on }[0,\tau].
$$
We consider the case when the right-hand side is nonconvex and the
constraint is moving.
Доводиться існування в сепарабельних банахових просторах розв'язків на всьому інтервалі для функціонально-диференціальних включень
$$
x^{(k)}(t) \in F(t,T(t)x,x^{(1)}(t),...,x^{(k-1)}(t)),\quad\mbox{a.e. on }[0,\tau].
$$
Розглядається випадок неопуклої правої частини та рухомого обмеження.
