PROBLEM ELLIPTIC ANISOTROPIC NONLINEAR IN RN WITH VARIABLE EXPONENT AND LOCALLY INTEGRABLE DATA
| dc.contributor.author | NOUREDDINE, DECHOUCHA | |
| dc.contributor.author | Supervisor: FARES, MOKHTARI | |
| dc.date.accessioned | 2025-11-30T08:11:54Z | |
| dc.date.available | 2025-11-30T08:11:54Z | |
| dc.date.issued | 2025-10-30 | |
| dc.description.abstract | This work is devoted to establishing the existence of weak solutions for a certain class of nonlinear anisotropic elliptic equations, where the involved exponents vary with po sition and the coercivity condition may degenerate. The equations under consideration take the following general form B(u) + H(x, u) = f, x ∈ R N , N ≥ 2 where f is locally integrable on R N and the operator B(u) = − N X i=1 Di(ei(x, u)bi(x, u, Du)) is properly defined between W0 1,p(.) (Ω), (Ω or R N )and its dual. Suppose that bi : R N ×R× R N −→ R, are a Carathéodory functions. The functions ei : R N × R −→ R are Carathéodory functions and satisfying the following condition η (1 + |u|) γi(x) ≤ ei(x, u) ≤ µ, where η, µ are strictly positeve real numbers and γi(x) ≥ 0, i = 1, ..., N are continuous functions on R N . And H : R N × R −→ R be a Carathéodory functions. The differential operetor B is not coercive if u is large. The core strategy of the proof involves deriving local estimates for a sequence of appro priately constructed approximate problems, followed by a limiting process. The findings presented here extend known results from the constant exponent framework and also build upon certain results discussed in [12]. | |
| dc.identifier.uri | https://repository.univ-msila.dz/handle/123456789/47870 | |
| dc.language.iso | en | |
| dc.publisher | University of Mohamed Boudiaf M'Sila | |
| dc.subject | Anisotropic equations | |
| dc.subject | Variable exponents | |
| dc.subject | Nonlinear elliptic problem | |
| dc.subject | Weak solutions | |
| dc.subject | Locally integrable data | |
| dc.title | PROBLEM ELLIPTIC ANISOTROPIC NONLINEAR IN RN WITH VARIABLE EXPONENT AND LOCALLY INTEGRABLE DATA | |
| dc.type | Thesis |