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In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.

In this paper, we present a lemma that allows us to characterize a broad class of C0-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞). [ABSTRACT FROM AUTHOR]

In this paper, we offer a new modelling approach for hepatitis C virus (HCV) infection models with cytotoxic T lymphocytes (CTL) immune responses. The standard neural network models with reaction-diffusion terms are generalized to the discontinuous case considering impulsive controllers. Also, the conformable approach is proposed as a more adjustable modelling apparatus which overcomes existing difficulties in the application of the fractional-order modelling technique. In addition, the existence of integral manifolds for the proposed model is investigated and efficient criteria are established. Since stability and control of a neural network model are essential for its proper application, stability results for the constructed integral manifold are presented. These results extend and generalize the stability results for steady states of proposed HCV models with CTL immune responses and contribute to the development of new innovative modelling approaches in biology. The qualitative analysis is performed via the conformable Lyapunov function method. The established results are demonstrated through an example. [ABSTRACT FROM AUTHOR]

This work offers a real-world application for the study of fuzzy dynamic equations. First, we propose the novel concept of granular delta differentiability for fuzzy-valued functions defined on time scales with the help of the relative distance measure fuzzy arithmetic and horizontal membership functions. Then, fundamental foundations of fuzzy calculus on time scales are provided. Discussion on the Malthusian model defined on particular time scales to illustrate the proposed approach is presented. [ABSTRACT FROM AUTHOR]

We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.