A global bifurcation result for a class of semipositone elliptic systems

作者：Chhetri M; Girg P^*

来源：Journal of Mathematical Analysis and Applications, 2017, 453(1): 255-270.

DOI：10.1016/j.jmaa.2017.04.001

• Elliptic systems
• Semipositone
• Bifurcation from infinity
• Continua of solutions
• Nodal properties
• Positive solutions

We consider a system of the form
-Delta u = lambda(theta(1)v(+) + f (v)) in Omega; }
-Delta v = lambda(theta(2)u(+) + g (u)) in Omega;
u = 0 = v on partial derivative Omega,
where s+ =(def) max{s, 0}, theta(1) and theta(2) are fixed positive constants, lambda is an element of R is the bifurcation parameter, and Omega subset of R-N (N > 1) is a bounded domain with smooth boundary partial derivative Omega (a bounded open interval if N = 1). The nonlinearities f,g : R -> R 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 lambda in a neighborhood containing the simple eigenvalue of the associated eigenvalue problem.

• 出版日期2017-9-1