Abstract
In this paper, we consider p-Laplacian systems with singular weights. Exploiting Amann type three solutions theorem for a singular system, we prove the existence, nonexistence, and multiplicity of positive solutions when nonlinear terms have a combined sublinear effect at ∞.MSC:35J55, 34B18.
Highlights
1 Introduction In this paper, we study one-dimensional p-Laplacian system with singular weights of the form
The first step is to investigate certain conditions on f and g to guarantee C regularity of solutions. Another difficulty is to show that a corresponding integral operator is bounded on the set of functions between upper and lower solutions in C [, ]
As an application of Theorem . , we study the existence, nonexistence, and multiplicity of positive radial solutions for the following quasilinear system on an exterior domain:
Summary
We study one-dimensional p-Laplacian system with singular weights of the form. The first step is to investigate certain conditions on f and g to guarantee C regularity of solutions Another difficulty is to show that a corresponding integral operator is bounded on the set of functions between upper and lower solutions in C [ , ]. The existence of positive solutions for such systems has been widely studied, for example, in [ ] and [ ] for second order ODE systems, in [ , , , , , , ] and [ ] for semilinear elliptic systems on a bounded domain and in [ , , ] and [ ] for p-Laplacian systems on a bounded domain. For C monotone functions f and g with lims→∞ f (s) = ∞ = lims→∞ g(s) and satisfying condition (f ), they proved that there exists λ* > such that the problem has at least one positive solution for λ > λ*.
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