Chapter 7 Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations

Rachůnková, Irena; Staněk, Svatoslav; Tvrdý, Milan

doi:10.1016/s1874-5725(06)80011-8

Cited by 43 publications

(34 citation statements)

References 96 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, in these therein, the nonlinearities are nonsingular, what would happen if the nonlinearity term is singular? It is of interest to note here that singular boundary value problems in the continuous case have been studied in great detail in the literature [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In 1987, Lazer and Solimini [7] firstly investigated the existence of the positive periodic solutions of the problem…”

Section: U(t − 1) + A(t)u(t) = F (T U(t)) + C(t) T ∈ Zmentioning

confidence: 99%

Positive periodic solutions of second-order difference equations with weak singularities

2012

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

Section: U(t − 1) + A(t)u(t) = F (T U(t)) + C(t) T ∈ Zmentioning

confidence: 99%

Positive periodic solutions of second-order difference equations with weak singularities

2012

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…For rather representative overview and references, see e.g. [15] or [16]. To our knowledge, up to now singular periodic impulsive problems have not been treated.…”

Section: Preliminariesmentioning

confidence: 99%

Singular periodic impulse problems

Halas

Tvrdý

2008

Nonlinear Oscill

View full text Add to dashboard Cite

Abstract.Existence principle for the impulsive periodic boundary value problem u + c u = g(x) + e(t), u(is established, where g ∈ C(0, ∞) can have a strong singularity at the origin. Furthermore, we assume that 0 < t 1 < . .The principle is based on an averaging procedure similar to that introduced by Manásevich and Mawhin for singular periodic problems with p -Laplacian in [11]. Mathematics Subject Classification 2000. 34B37, 34B15, 34C25 Keywords. impulses, periodic solutions, topological degree PreliminariesStarting with Hu and Lakshmikantham [7], periodic boundary value problems for nonlinear second order impulsive differential equations of the formhave been studied by many authors. Usually it is assumed that the function f : [0, T ] × R 2 → R fulfils the Carathéodory conditions, 0 < t 1 < t 2 < . . . < t m < T are fixed points of the interval [0, T ] (1.4) 1

show abstract

“…They also appear in the study of positive radial solutions of nonlinear elliptic equations. Therefore, they have been extensively studied in recent years, see, for instance, [1]- [5], [8], [13] and references therein. After studying singular two-point BVPs in detail, some authors began to pay attention to singular multi-point BVPs [9]- [12], [14]- [17].…”

Section: Introductionmentioning

confidence: 99%

Existence of positive solutions for singular four-point boundary value problem with a p-Laplacian

Miao

Zhao

2009

Czech Math J

View full text Add to dashboard Cite

Chapter 7 Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations

Cited by 43 publications

References 96 publications

Positive periodic solutions of second-order difference equations with weak singularities

Positive periodic solutions of second-order difference equations with weak singularities

Singular periodic impulse problems

Existence of positive solutions for singular four-point boundary value problem with a p-Laplacian

Contact Info

Product

Resources

About