منابع مشابه
Sturm-liouville Problems
Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.
متن کاملInverse Spectral Problems for Nonlinear Sturm-liouville Problems
This paper concerns the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0, where λ is a positive parameter. We try to determine the nonlinear term f(u) by means of the global behavior of the bifurcation branch of the positive solutions in R+ × L2(I).
متن کاملSpectral asymptotics for inverse nonlinear Sturm-Liouville problems
We consider the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t), u′(t)) = λu(t), u(t) > 0, t ∈ I := (−1/2, 1/2), u(±1/2) = 0, where f(x, y) = |x|p−1x − |y|m, p > 1, 1 ≤ m < 2 are constants and λ > 0 is an eigenvalue parameter. To understand well the global structure of the bifurcation branch of positive solutions in R+ ×Lq(I) (1 ≤ q < ∞) from a viewpoint of inverse problems, we establish the...
متن کاملAdomian Decomposition Method for Nonlinear Sturm-liouville Problems
In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
متن کاملGlobal Bifurcation in Generic Systems of Nonlinear Sturm-liouville Problems
We consider the system of coupled nonlinear Sturm-Liouville boundary value problems L1u := −(p1u′)′ + q1u = μu + uf(·, u, v), in (0, 1), a10u(0) + b10u′(0) = 0, a11u(1) + b11u′(1) = 0, L2v := −(p2v′)′ + q2v = νv + vg(·, u, v), in (0, 1), a20v(0) + b20v′(0) = 0, a21v(1) + b21v′(1) = 0, where μ, ν are real spectral parameters. It will be shown that if the functions f and g are ‘generic’ then for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1971
ISSN: 0022-0396
DOI: 10.1016/0022-0396(71)90101-x