# Registered Data

Contents

- 1 [CT019]
- 1.1 [00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator
- 1.2 [00018] Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting
- 1.3 [01883] An application to the generalized logistic growth model
- 1.4 [01155] Optimal bounds on the fundamental spectral gap with single-well potentials
- 1.5 [00128] A Numerical Approximation for Generalized Fractional Sturm-Liouville Problem with Application

# [CT019]

## [00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We study the shape of bifurcation curve of positive solutions for the semipositone Minkowski-curvature problem $-\left( u^{\prime }/\sqrt{1-{u^{\prime }}^{2}}\right) ^{\prime }=\lambda f(u),$ in $\left( -L,L\right) $, and $u(-L)=u(L)=0,$ where $\lambda ,L>0$ and $\left( \beta -u\right) f(u)<0$ for $u>0$. We prove that if $f$ is either convex or concave, then the bifurcation curve is C-shaped.**Classification**:__34B15__,__34B18__,__34C23__,__74G35__**Author(s)**:**Shao-Yuan Huang**(National Taipei University of Education)

## [00018] Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We study the diffusive generalized logistic problem with constant yield harvesting: \begin{equation*} \left \{ \begin{array}{ll} u^{\prime \prime }(x)+\lambda g(u)-\mu =0, & -10$. We prove that, for any fixed $\mu >0,$ on the $(\lambda ,\left \Vert u\right \Vert _{\infty })$-plane, the bifurcation diagram consists of a $\subset $-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying $\mu >0.$ **Classification**:__34B18__,__74G35__**Author(s)**:**Shin-Hwa Wang**(National Tsing Hua University, TAIWAN)- Kuo-Chih Hung (National Chin-Yi University of Technology, Taiwan)
- Yiu-Nam Suen (National Tsing Hua University, TAIWAN)

## [01883] An application to the generalized logistic growth model

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We study the bifurcation curves for a Dirichlet problem with geometrically concave nonlinearity. We give an application to the generalized logistic growth model. There are totally six qualitatively bifurcation curves.**Classification**:__34B18__,__74G35__**Author(s)**:**Kuo-Chih Hung**(National Chin-Yi University of Technology)- Kuo-Chih Hung (National Chin-Yi University of Technology)

## [01155] Optimal bounds on the fundamental spectral gap with single-well potentials

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We characterize the potential-energy functions $V(x)$ that minimize the gap $\Gamma$ between the two lowest Sturm-Liouville eigenvalues for \[ H(p,V) u := -\frac{d}{dx} \left(p(x)\frac{du}{dx}\right)+V(x) u = \lambda u, \quad\quad x\in [0,\pi ], \] where separated self-adjoint boundary conditions are imposed at end points, and $V$ is subject to various assumptions, especially convexity or having a ``single-well'' form. In the classic case where $p=1$ we recover with different arguments the result of Lavine that $\Gamma$ is uniquely minimized among convex $V$ by the constant, and in the case of single-well potentials, with no restrictions on the position of the minimum, we obtain a new, sharp bound, that $\Gamma > 2.04575\dots$.**Classification**:__34B27__,__35J60__,__35B05__**Author(s)**:**Zakaria El Allali**(Mohammed First University , Oujda, Morocco)- Evans Harrell (Georgia Institute of Technology)

## [00128] A Numerical Approximation for Generalized Fractional Sturm-Liouville Problem with Application

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: In this paper, we present a numerical scheme for the generalized fractional Sturm-Liouville problem (GFSLP) with mixed boundary conditions. The GFSLP is defined in terms of a B-operator consisting of an integral operator with a kernel and a differential operator. One of the main features of the B-operator is that for different kernels, it leads to different Sturm-Liouville Problems (SLPs), and thus the same formulation can be used to discuss different SLPs. We prove the well-posedness of the proposed GFSLP. Further, the approximated eigenvalues of GFSLP are obtained for two different kernels namely a modified power kernel and Prabhakar kernel in the B-operator. We obtain real eigenvalues and corresponding orthogonal eigenfunctions. The theoretical and numerical convergence orders of eigenvalues and eigenvectors are also discussed. Further, the numerically obtained eigenvalues and eigenfunctions are used to construct an approximate solution of the one-dimensional fractional diffusion equation defined in a bounded domain.**Classification**:__34L16__,__34L10__,__34L15__**Author(s)**:**Eti Goel**(Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi, Uttar Pradesh, India)- Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi, Uttar Pradesh, India)