Results 21 to 30 of about 5,326 (220)
THE NEW ASYMPTOTICS FOR SOLUTIONS OF THE STURM–LIOUVILLE EQUATION
Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2023 Summary: In this paper, we show the development of a method that allows one to construct asymptotics for solutions to ordinary differential equations of arbitrary order with oscillating coefficients on the semiaxis. The idea of the method is presented on the example of studying the asymptotics of the Sturm-Liouville equation solutions.
Nazirova, Elvira A. +2 more
openaire +1 more source
Journal of Mathematics, 2021 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 ...
Dan Liu, Xuejun Zhang, Mingliang Song
doaj +1 more source
On the structure of (2+1)-dimensional commutative and noncommutative integrable equations [PDF]
, 2006 We develop the symbolic representation method to derive the hierarchies of (2+1)-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the
Jing Ping Wang, Wang, Jing Ping
core +1 more source
Mathematics, 2020 The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov.
Oktay Sh. Mukhtarov, Merve Yücel
doaj +1 more source
Stability of stationary solutions for nonintegrable peakon equations [PDF]
, 2014 The Camassa-Holm equation with linear dispersion was originally derived as an asymptotic equation in shallow water wave theory. Among its many interesting mathematical properties, which include complete integrability, perhaps the most striking is the ...
S. Lafortune +3 more
core +1 more source
, 2021 In Chap. 3 we have seen how the separability of PDEs leads to ordinary differential equations problems, usually of second order. The problem is complemented with B.C.s and the reduction of the initial PDE to second order ODEs often yield a so-called
Cossali G., Tonini S.
core +1 more source
Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations [PDF]
Opuscula MathematicaIn this study, we addressed the nonoscillation of th Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type
Kazuki Ishibashi
doaj +1 more source
On strong singular fractional version of the Sturm–Liouville equation
Boundary Value Problems, 2021 The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewed, but one of its most attractive versions is
Mehdi Shabibi +3 more
doaj +1 more source
Solutions of Sturm-Liouville Problems
, 2020 This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems.
Christine Böckmann, Upeksha Perera
core +1 more source
Indefinite Hamiltonian systems whose Titchmarsh–Weyl coefficients have no finite generalized poles of non-positive type [PDF]
, 2013 The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H takes non-negative 2x2-matrices as values, and $J:= \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$, has attracted a lot of interest over the past decades ...
Harald Woracek +3 more
core +1 more source