Generating an arbitrarily large number of isolas in a superlinear indefinite problem

A class of nonlocal indefinite differential systems

“…Remark 4.1 In Theorem 3.1 and Theorem 3.2, we generalize the results of [38][39][40][41][42][43] in three main directions:…”

“…Moreover, a class of indefinite problems have attracted the attention of Ma and Han [38], López-Gómez and Tellini [39], Boscaggin and Zanolin [40,41], Sovrano and Zanolin [42], Bravo and Torres [43], Wang and An [44], and Yao [45]. In [38], Ma and Han considered the following boundary value problem:…”

High multiplicity of positive solutions for superlinear indefinite problems with homogeneous Neumann boundary conditions

“…Remark 5.2. It is possible to adapt the analysis of [18,24] to study the case in which the weight function a(t) in (1.1) is asymmetric of the form…”

“…A remarkable novel result is that, when λ is sufficiently negative, the bifurcation diagrams always exhibit several isolated bounded components (see Theorem 5.1 and Figure 6), whose number can be arbitrarily high. On the contrary, when b is used as the main bifurcation parameter, this phenomenon is typically related to the presence of asymmetric weights, as shown in [18] for Dirichlet boundary conditions, and does not happen in the case of symmetric weights treated in [19]. Still, considering asymmetric weights in the case of Neumann boundary condition further increases the number of components, as a consequence of the breaking of secondary bifurcation points (see Remark 5.2).…”

Imperfect bifurcations via topological methods in superlinear indefinite problems

“…In this work we give a deeper insight on this phenomenon, studying how the secondary bifurcations break as the weight is perturbed from the symmetric situation. Our proofs rely on the approach of [5,4], i.e. on the construction of certain Poincaré maps and the study of how they vary as some of the parameters of the problems change, constructing in this way the bifurcation diagrams.…”