Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774958 | Journal of Mathematical Analysis and Applications | 2017 | 16 Pages |
Abstract
We consider a system of the formâÎu=λ(θ1v++f(v))inΩ;âÎv=λ(θ2u++g(u))inΩ;u=0=vonâΩ,} where s+=defmaxâ¡{s,0}, θ1 and θ2 are fixed positive constants, λâR is the bifurcation parameter, and ΩâRN (N>1) is a bounded domain with smooth boundary âΩ (a bounded open interval if N=1). The nonlinearities f,g:RâR are continuous functions that are bounded from below, sublinear at infinity and have semipositone structure at the origin (f(0),g(0)<0). We show that there are two disjoint unbounded connected components of the solution set and discuss the nodal properties of solutions on these components. Finally, as a consequence of these results, we infer the existence and multiplicity of solutions for λ in a neighborhood containing the simple eigenvalue of the associated eigenvalue problem.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Chhetri, P. Girg,