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We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge-Amp\`ere operator on a bounded strongly pseudoconvex domain in $\C^n$. We show that the eigenfunction is…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this…
We examine the regularity of the extremal solution of the nonlinear eigenvalue problem $\Delta^2 u = \lambda f(u)$ on a general bounded domain $\Omega$ in $ \IR^N$, with the Navier boundary condition $ u=\Delta u =0 $ on $ \pOm$. Here $…
We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We consider four definitions of solution to the initial-boundary value problem for a scalar balance laws in several space dimensions. These definitions are generalised to the same most general framework and then compared. The first aim of…
We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We prove global existence and blow-up of solutions of initial-boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
We formulate on a half-strip an initial boundary value problem for the two-dmensional Kawahara equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the elevated norm of small solutions are…
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $\alpha\in(2,3)$, involving a general form of fractional derivative. First, we prove an…