Weak solutions for generalized p-Laplacian systems via Young measures

Existence of weak solutions for a class of (p,q)$(p,q)$-Laplacian systems

Nontrivial solutions for p-Laplacian systems

The paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div (|∇ui |p−2∇ui)+ λfi(u1, . . . , un)= 0 in Ω, ui = 0 on ∂Ω, i = 1, . . . , n, where p > 1, Ω is a bounded domain in RN (N 2) with smooth boundary, and fi , i = 1, . . . , n, are continuous, nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1 |ui |, we prove t...

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...

Existence of Positive Solutions for Generalized p-Laplacian BVPs

Using Kransnoskii’s fixed point theorem, the authors obtain the existence of multiple solutions of the following boundary value problem ( ) ( ) , , ..., = 0, 0,1 1 2 BVP E u t f t u t u t t p n n φ − ( ) − ( ) ( ) ( ) ( ) + ( ) ( ) ( ) ∈ ( ) ' , ( ) 0 = 0, 0 3, 0 = 0, 1 2 0 1 2 BC u i n u B u u i

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...