N. Askouraye

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Articles: 1

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.

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