Vol. 30 No. 2 (2023)

Open Access

Articles

Article ID: 2405

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION FOR RAYLEIGH TYPE p-LAPLACIAN EQUATION

by Congmin Yang, Zhihang Xu, Zaihong Wang

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

In this paper, we study the existence and uniqueness of periodic solution for Rayleigh type $p$-Laplacian equation $$\left(\phi_p\left(x^{\prime}(t)\right)\right)^{\prime}+f\left(t, x^{\prime}(t)\right)+g(t, x(t))=e(t)$$We prove the existence and uniqueness of periodic solution of the given equation provided that there exist constants $a>0, b>0$ such that $$|f(t, s)| \leq a|s|^{p-1}+b, \forall(t, s) \in \mathbb{R}^2$$ or $f$ is bounded below (or above) and $g$ satisfies the monotonicity condition.

Open Access

Articles

Article ID: 2406

EXISTENCE OF FIXED POINT FOR NONLINEAR OPERATOR IN PARTIALLY ORDERED METRIC SPACES

by Yan Sun, Ravi P. Agarwal

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

In this article, first we introduce new notions of a contractive mapping and establish some fixed point theorems for the contractive mapping in the setting of LG-complete LG-metric spaces. Further, we establish a new criterion between weakly regular cone and normal cone, and we also obtain a fixed point result in the same LG-complete LG-metric spaces by making use of analysis technique. Later, we give some examples to illustrate the valid of our main results.

Open Access

Articles

Article ID: 2407

ANALYSIS OF GENERALIZED FINITE CONTINUOUS RIDGELET TRANSFORMS WITH SIMPLY SUPPORTED RECTANGULAR KIRCHHOFF PLATES

by Nitu Gupta, V. R. Lakshmi Gorty

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

This work presents the application of generalized finite continuous Ridgelet transform (GFCRT). The solution of Kirchhoff plates with rectangular and simply supported obeying Dirichlet boundary conditions is demonstrated using GFCRT. The inversion formula when applied to the stated problem represents an algebraic solution. In the concluding section, the obtained numerical results are discussed with uniformly distributed patch load, general distributed load and point load.

Open Access

Articles

Article ID: 2408

OPTIMAL CONTROL OF A NONLINEAR ELLIPTICAL EVOLUTION PROBLEM WITH MISSING DATA

by Thomas TINDANO, Mifiamba SOMA, Sadou TAO, Somdouda SAWADOGO

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

We consider the optimal control of a nonlinear elliptic problem with missing data (so-called ill-posed problems). Using the notion of no-regret and low-regret control, we give a characterization of the control for ill-posed problems. More precisely, we study the control of Cauchy evolution problems via a regularization approach which generates incomplete information. We obtain a singular optimality system characterizing the no-regret control for the Cauchy evolution problems.

Open Access

Articles

Article ID: 2409

CONVERGENCE AND APPLICATION OF A MODIFIED DOUBLE LAPLACE TRANSFORM (MDLT) IN SOME EQUATIONS OF MATHEMATICAL PHYSICS

by Tarig M. Elzaki, Mourad Chamekh, Shams A. Ahmed

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

Dealing with a modified double Laplace transform (MDLT) technique, we have established some convergence results. Then, using this new technique, we propose resolutions of some equations such as pseudo-hyperbolic and the Benney-Luke equations. The advantage of MDLT is that we can obtain exact solutions in one step. The technique aims to provide viable results with respect to particular cases. Finally, some numerical results are presented.

Open Access

Articles

Article ID: 2410

ON REALIZATION OF THE SUPERPOSITION PRINCIPLE FOR A FINITE BUNDLE OF INTEGRAL CURVES OF A SECOND-ORDER BILINEAR DIFFERENTIAL SYSTEM

by A. V. Lakeyev, V. A. Rusanov, A. V. Daneev, Yu. D. Aksenov

Advances in Differential Equations and Control Processes, Vol.30, No.2, 2023;

We investigate the solvability of the problem of realization of operator-functions of invariant linear regulator (IL-regulator) of a second order nonstationary differential system (D-system), which allows for a finite bundle of integral curves of “trajectory, control” type, induced in this D-system by different bilinear regulators, to reduce this bundle to a subfamily of admissible solutions of this D-system through action of IL-regulator. The problem under consideration belongs to the type of nonstationary coefficient-operator inverse problems for evolution equations (including the hyperbolic) in separable Hilbert space. The problem is solved on the basis of a qualitative study of the continuity and semiadditivity properties of the nonlinear Rayleigh-Ritz functional operator. The obtained results have applications in the theory of nonlinear infinite-dimensional adaptive dynamical systems for a class of bilinear differential models of higher orders.