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In this paper, we study the existence of positive solutions for a nonlocal singular elliptic coupled system involving N-Laplace operator. The source term of the system is expressed as the sum of two components: one with subcritical, critical, or supercritical exponential growth controlled by the Trudinger–Moser inequality, and the other being singular at the origin. We also investigate the asymptotic behavior of the solutions with respect to the parameters. Furthermore, we prove that no solutions exist for our system in dimension N = 2 . [ABSTRACT FROM AUTHOR]

This work investigates positive solutions for equations involving the anisotropic variable exponent operator, a mathematical framework critical in modeling nonstandard growth phenomena. By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. These findings have significant implications for real-world applications, such as fluid dynamics, image processing, and material science, where variable growth conditions arise naturally. More specifically, the study employs methods from functional analysis to investigate the existence, nonexistence, and minimal solutions of certain anisotropic equations within the framework of generalized Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results. [ABSTRACT FROM AUTHOR]

We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up. [ABSTRACT FROM AUTHOR]

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space. [ABSTRACT FROM AUTHOR]

This work studies the three space dimensional focusing inhomogeneous Schrödinger equation with inverse square potential i ∂ t u − (− Δ + λ | x | 2 ) u + | x | − 2 τ | u | 2 (q − 1) u = 0 , u (t , x) : R × R 3 → C. The purpose is to investigate the energy scattering of global inter-critical solutions below the ground state threshold. The scattering is obtained by using the new approach of Dodson-Murphy, based on Tao's scattering criteria and Morawetz estimates. This work naturally extends the recent paper by J. An et al. (Discrete Contin. Dyn. Syst., Ser. B 28(2): 1046–1067 2023). The threshold is expressed in terms the non-conserved potential energy. As a consequence, it can be given with a classical way with the conserved mass and energy. The inhomogeneous term | x | − 2 τ for τ > 0 guarantees the existence of ground states for λ ≥ 0 , contrarily to the homogeneous case τ = 0 . Moreover, the decay of the inhomogeneous term enables to avoid any radial assumption on the datum. Since there is no dispersive estimate of L 1 → L ∞ for the free Schrödinger equation with inverse square potential for λ < 0 , one restricts this work to the case λ ≥ 0 . [ABSTRACT FROM AUTHOR]