Positive solutions for asymptotically linear problems in exterior domains

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

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

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.

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 Super-solutions to Semi-linear Second-order Non-divergence Type Elliptic Equations in Exterior Domains

We study the problem of the existence and non-existence of positive super-solutions to a semi-linear second-order non-divergence type elliptic equation ∑N i,j=1 aij(x) ∂2u ∂xi∂xj + up = 0, −∞ < p < ∞, with measurable coefficients in exterior domains of RN . We prove that in a “generic” situation there is one critical value of p that separates the existence region from nonexistence. We reveal th...