Discontinuous Sturm-Liouville Problems and Associated Sampling Theories by M. M. Tharwat

“…We closely follow the analysis derived by Fulton (1977) to establish the needed relations for the derivations of the sampling theorems including the construction of Green's function as well as the eigenfunction expansion theorem. …”
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Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse by Rauf Kh. Amırov, A. Adiloglu Nabıev

“…In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. …”
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Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space by Hua Su, Lishan Liu, Yonghong Wu

“…We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. …”
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Existence of Solutions for Sturm-Liouville Boundary Value Problem of Impulsive Differential Equations by Hong-Rui Sun, Ya-Ning Li, Juan J. Nieto, Qing Tang

“…The main tools are variational method and critical point theorems. Some examples are also given to illustrate the main results.…”
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Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
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Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter by Elgiz Bairamov, M. Seyyit Seyyidoglu

“…In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of 𝐴. …”
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Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero by Dan Liu, Xuejun Zhang, Mingliang Song

“…We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x,  a.e. t∈0,1x0cos  α−P0x′0sin  α=0x1cos  β−P1x′1sin  β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem of Schechter and the symmetric mountain pass theorem of Kajikiya. …”
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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation by Yanan Li, Shurong Sun, Zhenlai Han, Hongling Lu

“…By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. …”
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Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line by Yanmei Sun, Zengqin Zhao

“…By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. …”
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A representation theorem for the linear quasi-differential equation (py′)′+qy=0 by J. G. O'Hara

“…We give a number of applications, including a simple proof of Sturm's comparison theorem.…”
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Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals by Hairong Lian, Junfang Zhao

“…We generalize the unbounded upper and lower solution method to a third-order ordinary differential equation on the half line subject to the Sturm-Liouville boundary conditions. By using such techniques and the Schäuder fixed point theorem, some criteria are presented for the existence of solutions and positive ones to the problem discussed.…”
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Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications” by Ziyatkhan Aliyev

“…Moreover, they also establish the Sturm type comparison theorem for fourth-order problems with sign-changing weight. …”
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Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications by Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji

“…Then, existence and uniqueness theorems for the Caputo (CFC) and Riemann (CFR) type initial difference value problems by using Banach contraction theorem are proved. …”
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