Positive solution of asymptotically linear elliptic eigenvalue problems for certain differential equations of the fourth order
Some properties of solutions of elliptic partial differential equations of the second order
Global inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation of second order
Dependence of a differential equation on the first eigenvalue of a suitable problem
On some linear eigenvalue problems for strongly elliptic systems with an indefinite weight matrix function
Oscillation theorems and nodes of eigenfunctions of certain differential equations of the fourth order
On some problems in the theory of eigenvalues and eigenfunctions associated with linear elliptic partial differential equations of the second order
On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation
Semilinear evolution equations of the parabolic type
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
An abstract semilinear first order differential equation in the hyperbolic case
This paper is devoted to the investigation of the abstract semilinear initial value problem , in the “hyperbolic” case.
Existence of the fundamental solution of a second order evolution equation
We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence of bounded operators.
Second order semilinear Volterra integrodifferential equation in Banach space
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
An abstract nonlinear second order differential equation
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
Existence of a minimal solution and a maximal solution of a nonlinear elliptic boundary value problem of the fourth order
On the inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation with constant coefficients of the second order
On eigenvalues and eigenfunctions of an operational equation
Nodes of eigenfunctions of a certain class of ordinary differential equations of the fourth order
On some properties of eigenvalues and eigenfunctions of certain differential equations of the fourth order
On positive eigenvectors of a linear eigenvalue problem
Evolution equations with parameter in the hyperbolic case
The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter in the “hyperbolic” case.
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