Resonances of third order differential operators
نویسندگان
چکیده
منابع مشابه
a class of fourth order differential operators with transmission conditions
we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...
متن کاملOn the Invariant Properties of Hyperbolic Bivariate Third-Order Linear Partial Differential Operators
Bivariate, hyperbolic third-order linear partial differential operators under the gauge transformations L → g(x, y)−1 ◦ L ◦ g(x, y) are considered. The existence of a factorization, the existence of a factorization that extends a given factorization of the symbol of the operator, and the existence of factorizations with special properties appearing through the consideration of the intersection ...
متن کاملA Full System of Invariants for Third-Order Linear Partial Differential Operators in General Form
We find a full system of invariants with respect to gauge transformations L → g−1Lg for third-order hyperbolic linear partial differential operators on the plane. The operators are considered in a normalized form, in which they have the symbol SymL = (pX + qY )XY for some non-zero bivariate functions p and q. For this normalized form, explicit formulae are given. The paper generalizes a previou...
متن کاملOscillation of Third-order Functional Differential Equations
The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation (E) ˆ a(t) ˆ x ′′(t) ̃ γ ̃ ′ + q(t)f(x [τ (t)]) = 0. Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (E). Obtained results essentially improve and complement earlier ones. Variou...
متن کاملLiouvillian solutions of third order differential equations
The Kovacic algorithm and its improvements give explicit formulae for the Liouvillian solutions of second order linear differential equations. Algorithms for third order differential equations also exist, but the tools they use are more sophisticated and the computations more involved. In this paper we refine parts of the algorithm to find Liouvillian solutions of third order equations. We show...
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 Mathematical Analysis and Applications
سال: 2019
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.05.007