Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition

Benaissa, S., Messelmi, F., Merouani, A.

O‘zbekiston matematika jurnali · 2026-yil

Annotatsiya

In this work, we study a class of nonlinear elliptic equations of the form $Au=-\Delta _{p}u+ div \left( Vu\right) =R(x,u)$ in a bounded domain $\Omega \subset \mathbb{R}^n$, where $-\Delta _{p}u=- div \left( \left \vert \nabla u\right \vert ^{p-2}\nabla u\right)$ denotes the p-Laplacian operator, $V(x)$ is a given vector field, and $R(x)$ represents a source term. We establish the existence and uniqueness of weak solutions under suitable assumptions on $V$ and $R$. To establish the existence of weak solutions to the nonlinear elliptic problem we employ a fixed point approach based on the compactness of the associated operator. The existence result is obtained by proving that the composition $A^{-1}N_{R}$ is a compact and continuous mapping that admits at least one fixed point, where $N_{R}$ is the Nemyskii operator corresponding to a Caratheodory function $R$. This ensures the existence of a weak solution $u\in W_{0}^{1,p}\left( \Omega \right)$. For the uniqueness of solutions, we rely on the strict monotonicity of the p-Laplacian operator and appropriate growth and Lipschitz conditions on $R(x,u)$.

Maqola ma’lumotlari
MualliflarBenaissa, S., Messelmi, F., Merouani, A.
JurnalO‘zbekiston matematika jurnali
NashriyotЎзбекистон Республикаси ФА Математика институти
ISSN2010-7269
Nashr sanasi2026-07-02
Jild70
Son2
Betlar33-41
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.29229/uzmj.2026-2-4
Indeksga qo‘shilgan2026-08-26

DOI: 10.29229/uzmj.2026-2-4 · Maqolaning asl sahifasi

Kalit so‘zlar

p-Laplacian, Fixed point, Variational formulation, Caratheodory function, Nemytskii operator

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APABenaissa, S., Messelmi, F., & Merouani, A. (2026). Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition. O‘zbekiston matematika jurnali, 70(2), 33-41. https://doi.org/10.29229/uzmj.2026-2-4
GOST (OAK)Benaissa, S., Messelmi, F., Merouani, A. Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 33-41. – DOI: 10.29229/uzmj.2026-2-4.
MLABenaissa, S., Messelmi, F., and Merouani, A. “Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition.” O‘zbekiston matematika jurnali, 70(2), 33-41, 2026. https://doi.org/10.29229/uzmj.2026-2-4
ChicagoBenaissa, S., Messelmi, F., and Merouani, A. “Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition.” O‘zbekiston matematika jurnali, 70(2), 33-41 (2026). https://doi.org/10.29229/uzmj.2026-2-4
HarvardBenaissa, S., Messelmi, F., and Merouani, A (2026) ‘Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition’, O‘zbekiston matematika jurnali, 70(2), 33-41. https://doi.org/10.29229/uzmj.2026-2-4
BibTeX
@article{benaissas2026,
  title = {Solvability of a nonlinear elliptic problem involving $p-$Laplacian with Dirichlet condition},
  author = {Benaissa, S. and Messelmi, F. and Merouani, A.},
  journal = {O‘zbekiston matematika jurnali},
  year = {2026},
  volume = {70},
  number = {2},
  pages = {33-41},
  doi = {10.29229/uzmj.2026-2-4},
  url = {https://doi.org/10.29229/uzmj.2026-2-4}
}

Boshqa maqola uchun iqtibos tayyorlash

O‘zbekiston matematika jurnali jurnalidan boshqa maqolalar

O‘zbekiston matematika jurnali — barcha maqolalar · 2026-yil arxivi

Fizika-matematika sohasidagi boshqa maqolalar

Fizika-matematika sohasidagi OAK jurnallari