Multiplicity Results of Positive Radial Solutions for -Laplacian Problems in Exterior Domains

Multiplicity Results of Positive Radial Solutions for p-Laplacian Problems in Exterior Domains

Existence and Multiplicity of Positive Radial Solutions to Nonlocal Boundary-value Problems in Exterior Domains

In this article, we consider nonlocal p-Laplacian boundary-value problems with integral boundary conditions and a non-negative real-valued boundary condition as a parameter. The main purpose is to study the existence, nonexistence and multiplicity of positive solutions as the boundary parameter varies. Moreover, we prove a sub-super solution theorem, using fixed point index theorems.

POSITIVE SOLUTIONS OF INEQUALITY WITH p-LAPLACIAN IN EXTERIOR DOMAINS

In the paper the differential inequality ∆pu +B(x, u) 6 0, where ∆pu = div(‖∇u‖ ∇u), p > 1, B(x, u) ∈ C( n × , ) is studied. Sufficient conditions on the function B(x, u) are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

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...