Abstract
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.
Key words: Differential inclusion, boundary value problem, topological degree, lower semi-continuous
multifunction, measurability.
Full Text
Article Information
| Title | Existence of solutions for lower semi-continuous non-convex differential inclusions with $\phi-$Laplacian |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 1, 25-34 |
| DOI | 10.31392/MFAT-npu26_1.2026.04 |
| Milestones | Received 30/12/2024; Revised 07/01/2026 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Najib Askouraye
University Sultan Moulay Slimane, Faculty polydisciplinary, BP 145, Khouribga, Morocco.
Myelkebir Aitalioubrahim
University Sultan Moulay Slimane, Faculty polydisciplinary, BP 145, Khouribga, Morocco.
Citation Example
Najib Askouraye and Myelkebir Aitalioubrahim, Existence of solutions for lower semi-continuous non-convex differential inclusions with $\phi-$Laplacian, Methods Funct. Anal. Topology 32
(2026), no. 1, 25-34.
BibTex
@article {MFAT2209,
AUTHOR = {Najib Askouraye and Myelkebir Aitalioubrahim},
TITLE = {Existence of solutions for lower semi-continuous non-convex differential inclusions with $\phi-$Laplacian},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {1},
PAGES = {25-34},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2026.04},
URL = {https://mfat.imath.kiev.ua/article/?id=2209},
}
