@article{cronin_goddard ii_muthunayake_quiroa_shivaji_2024, title={Predator-induced prey dispersal can cause hump-shaped density-area relationships in prey populations}, volume={88}, ISSN={["1432-1416"]}, DOI={10.1007/s00285-023-02040-1}, number={2}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Cronin, James T. and Goddard Ii, Jerome and Muthunayake, Amila and Quiroa, Juan and Shivaji, Ratnasingham}, year={2024}, month={Feb} }
 @article{acharya_fonseka_quiroa_shivaji_2021, title={Σ</i>-Shaped Bifurcation Curves}, volume={10}, ISSN={2191-950X 2191-9496}, url={http://dx.doi.org/10.1515/anona-2020-0180}, DOI={10.1515/anona-2020-0180}, abstractNote={AbstractWe study positive solutions to the steady state reaction diffusion equation of the form:−Δu=λf(u); Ω∂u∂η+λu=0; ∂Ω$$\begin{array}{} \displaystyle \left\lbrace \begin{matrix} -{\it\Delta} u =\lambda f(u);~ {\it\Omega} \\ \frac{\partial u}{\partial \eta}+ \sqrt{\lambda} u=0;~\partial {\it\Omega}\end{matrix} \right. \end{array}$$whereλ> 0 is a positive parameter,Ωis a bounded domain in ℝNwhenN> 1 (with smooth boundary∂ Ω) orΩ= (0, 1), and∂u∂η$\begin{array}{} \displaystyle \frac{\partial u}{\partial \eta} \end{array}$is the outward normal derivative ofu. Heref(s) =ms+g(s) wherem≥ 0 (constant) andg∈C2[0,r) ∩C[0, ∞) for somer> 0. Further, we assume thatgis increasing, sublinear at infinity,g(0) = 0,g′(0) = 1 andg″(0) > 0. In particular, we discuss the existence of multiple positive solutions for certain ranges ofλleading to the occurrence ofΣ-shaped bifurcation diagrams. We establish our multiplicity results via the method of sub-supersolutions.}, number={1}, journal={Advances in Nonlinear Analysis}, publisher={Walter de Gruyter GmbH}, author={Acharya, A. and Fonseka, N. and Quiroa, J. and Shivaji, R.}, year={2021}, month={Jan}, pages={1255–1266} }