Abstract
We give a global description of the branches of positive solutions of first-order impulsive boundary value problem: which is not necessarily linearizable. Where is a parameter, are given impulsive points. Our approach is based on the Krein-Rutman theorem, topological degree, and global bifurcation techniques. MSC:34B10, 34B15, 34K15, 34K10, 34C25, 92D25.
Highlights
Some evolution processes are distinguished by the circumstance that at certain instants their evolution is subjected to a rapid change, that is, a jump in their states
We will apply the following global bifurcation theorems for mappings which are not necessarily smooth to get a global description of the branches of positive solutions of ( . ), ( . ), and we obtain the existence and multiplicity of positive solutions of ( . ), ( . )
Sections and are devoted to study the bifurcation from infinity and from the trivial solution for a nonlinear problem which are not necessarily linearizable, respectively
Summary
Some evolution processes are distinguished by the circumstance that at certain instants their evolution is subjected to a rapid change, that is, a jump in their states. (i) [λ (b∞), λ (b∞)] is a bifurcation interval of positive solutions from infinity for ), and there exists no bifurcation interval of positive solutions from infinity which is disjoint with [λ (b∞), λ (b∞)]. ), and there exists no bifurcation interval of positive solutions from the trivial solutions which is disjoint with [λ (a ), λ (a )]. [λ (b∞), λ (b∞)] is a unique bifurcation interval of positive solutions from infinity for We will apply the following global bifurcation theorems for mappings which are not necessarily smooth to get a global description of the branches of positive solutions of Sections and are devoted to study the bifurcation from infinity and from the trivial solution for a nonlinear problem which are not necessarily linearizable, respectively. In Section , we consider the intertwining of the branches bifurcating from infinity and from the trivial solution
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