A note on the existence of multiple solutions for a class of systems of second order ODEs

Boscaggin, Alberto; Dambrosio, Walter

doi:10.1016/j.jmaa.2014.01.085

Cited by 2 publications

(1 citation statement)

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“…Indeed, their flexibility is one of the advantages of the application of topological methods. The employment of topological tools to generalize existence results for ODEs to systems of differential equations obtained by suitable coupling of the original equation has been recently applied in various frameworks, for instance in [6,19,20,21]. We remark that such results are not necessarily restricted to small perturbations: indeed, as in our case, they apply also to larger suitable couplings.…”

Section: Introductionmentioning

confidence: 75%

Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model

Feltrin

Gidoni

2020

Nonlinear Analysis: Real World Applications

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We investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of the Neumann boundary value problemwhere the coupling-weights wi are sign-changing in the first variable, and the nonlinearities fi : [0, 1] → [0, +∞[ satisfy fi(0) = fi(1) = 0, fi(s) > 0 for all s ∈ ]0, 1[, and a superlinear growth condition at zero. Using a topological degree approach, we prove existence of 2 N positive fully nontrivial solutions when the real positive parameters λ1 and λ2 are sufficiently large.Mathematics Subject Classification (2010). 34B18, 47H11, 92D25.

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Section: Introductionmentioning

confidence: 75%