Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Powiadomienia systemowe

Sesja wygasła!

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially “dominated” nonlinearity and singular weight

Baraket Sami, Mahdaoui Safia, Ouni Taieb

Opuscula Mathematica

2023

Vol. 43, no. 1

5--18

Let Ω be a bounded domain in R4 with smooth boundary and let x1, x2, . . . , xm be m-points in Ω. We are concerned with the problem [formula], where the principal term is the bi-Laplacian operator, H(x, u, Dku) is a functional which grows with respect to Du at most like |Du|q, 1 ≤ q ≤ 4, f : Ω → [0,+∞[ is a smooth function satisfying f(pi) > 0 for any i = 1, . . . , n, αi are positives numbers and g : R → [0,+∞[ satisfy |g(u)| ≤ ceu. In this paper, we give sufficient conditions for existence of a family of positive weak solutions (uρ) ρ>0 in Ω under Navier boundary conditions u = Δu = 0 on ∂Ω. The solutions we constructed are singular as the parameters ρ tends to 0, when the set of concentration S = {x1, . . . , xm} ⊂ Ω and the set Λ := {p1, . . . , pn} ⊂ Ω are not necessarily disjoint. The proof is mainly based on nonlinear domain decomposition method.

On a weighted elliptic equation of N-Kirchhoff type with double exponential growth

Abid Imed, Baraket Sami, Jaidane Rached

Demonstratio Mathematica

2022

Vol. 55, nr 1

634--657

In this work, we study the weighted Kirchhoff problem (…) where B is the unit ball of RN , σ(x)=(log(e∣x∣))N−1 , the singular logarithm weight in the Trudinger-Moser embedding, and g is a continuous positive function on R+ . The nonlinearity is critical or subcritical growth in view of Trudinger-Moser inequalities. We first obtain the existence of a solution in the subcritical exponential growth case with positive energy by using minimax techniques combined with the Trudinger-Moser inequality. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth, and we stress its importance to check the compactness level.