排序方式: 共有19条查询结果,搜索用时 16 毫秒
1.
Ravi P. Agarwal Donal O’Regan Svatoslav Staněk 《Central European Journal of Mathematics》2009,7(4):694-716
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary
value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0. 相似文献
2.
The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular
Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.
This work was supported by grant no. A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic and by
the Council of Czech Government MSM 6198959214. 相似文献
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4.
We investigate the existence of positive solutions to the singular fractional boundary value problem: $^c\hspace{-1.0pt}D^{\alpha }u +f(t,u,u^{\prime },^c\hspace{-2.0pt}D^{\mu }u)=0$, u′(0) = 0, u(1) = 0, where 1 < α < 2, 0 < μ < 1, f is a Lq‐Carathéodory function, $q > \frac{1}{\alpha -1}$, and f(t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here $^c \hspace{-1.0pt}D$ stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones. 相似文献
5.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 相似文献
6.
Svatoslav Staněk 《Journal of Differential Equations》1978,30(3):287-295
This paper gives a generalization of the Sturm comparison theorem for differential equations (p): y″ = p(t)y, (q): y″ = q(t)y under the assumption that the function p ? q changes its sign exactly once on [a, b] or ∝tbp ? q, ∝atp ? q maintain the sign on [a, b]. The results are used for investigating the distributions of zeros of solutions and the derivative of solutions of (p), (q). 相似文献
7.
Svatoslav Stanêk 《Mathematische Nachrichten》1993,164(1):333-344
Using the Leray-Schauder degree method sufficient conditions for the one-parameter boundary value problem x″ = f(t, x, x′, λ), α(x) = A, x(0) ? x(1) = B, x′(0) ? x′(1) = C, are stated. The application is given for a class of functional boundary value problems for nonlinear third-order functional differential equations depending on the parameter. 相似文献
8.
Irena Rach?nková Svatoslav Staněk 《Journal of Mathematical Analysis and Applications》2004,291(2):741-756
The odd-order differential equation (−1)nx(2n+1)=f(t,x,…,x(2n)) together with the Lidstone boundary conditions x(2j)(0)=x(2j)(T)=0, 0?j?n−1, and the next condition x(2n)(0)=0 is discussed. Here f satisfying the local Carathéodory conditions can have singularities at the value zero of all its phase variables. Existence result for the above problem is proved by the general existence principle for singular boundary value problems. 相似文献
9.
Svatoslav Staněk 《Central European Journal of Mathematics》2014,12(11):1638-1655
In the first part, we investigate the singular BVP \(\tfrac{d} {{dt}}^c D^\alpha u + (a/t)^c D^\alpha u = \mathcal{H}u\) , u(0) = A, u(1) = B, c D α u(t)| t=0 = 0, where \(\mathcal{H}\) is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems \(\tfrac{d} {{dt}}^c D^{\alpha _n } u + (a/t)^c D^{\alpha _n } u = f(t,u,^c D^{\beta _n } u)\) , u(0) = A, u(1) = B, \(\left. {^c D^{\alpha _n } u(t)} \right|_{t = 0} = 0\) where a < 0, 0 < β n ≤ α n < 1, lim n→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying the boundary conditions u(0) = A, u(1) = B, u′(0) = 0. 相似文献
10.
Svatoslav Stanêk 《Mathematische Nachrichten》1998,192(1):225-237
A functional differential equation of the type where F: C1(J) → L1(J) is a unbounded operator, is considered. Sufficient conditions for the existence of at least two different solutions satisfying boundary conditions min{x(t): t ? J} = α, max{x(t): t ? J} = β are given. 相似文献