Positive solutions for a class of p-Laplacian systems with multiple parameters

Multiple Solutions for a Class of p(x)-Laplacian Systems

Since the space L x and W1,p x were thoroughly studied by Kováčik and Rákosnı́k 1 , variable exponent Sobolev spaces have been used in the last decades to model various phenomena. In 2 , Růžička presented the mathematical theory for the application of variable exponent spaces in electro-rheological fluids. In recent years, the differential equations and variational problems with p x -growth cond...

ON POSITIVE SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS INVOLVING THE p(x)-LAPLACIAN WITH MULTIPLE PARAMETERS

On Positive Solutions for a Class of p-Laplacian Problems

We consider the system ⎧ ⎪ ⎨ ⎪ ⎩ −Δ p u = λf (v) in Ω −Δ q v = μg(u) in Ω u = v = 0 on ∂Ω (I) where Δ p u = div(|∇u| p−2 ∇u), Δ q v = div(|∇v| q−2 ∇v), p, q > 1, Ω is the open unit ball in R N , N ≥ 2 and ∂Ω is its boundary. We establish upper and lower estimates for possible positive solutions of system(I).

Positive radial solutions for p-Laplacian systems

The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1...

Positive Solutions for a Class of p-Laplacian Systems with Sign-Changing Weight

We consider the system ⎧ ⎨ ⎩ −Δ p u = λF (x, u, v), x ∈ Ω, −Δ q v = λH(x, u, v), x ∈ Ω, u = 0 = v, x ∈ ∂Ω, where F (x, u, v) = [g(x)a(u) + f (v)], H(x, u, v) = [g(x)b(v) + h(u)], Ω is a bounded domain in R N (N ≥ 1) with smooth boundary ∂Ω, λ is a real positive parameter and Δ s z = div (|∇z| s−2 ∇z), s > 1, (s = p, q) is a s-laplacian operator. Here g is a C 1 sign-changing function that may b...