In this study, a global solution is presented for an initial boundary value problem involving a wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. The solution is obtained through the application of the energy method combined with the Faedo-Galarkin procedure. Additionally, a blow-up result for the solution is established, contingent upon the condition of non-positive initial energy.

In this research work, a sub-supersolution approach is utilized to investigate the existence and nonexistence of weak positive solution for a class of fractional Laplacian Kirchhoff type elliptic systems in bounded domains with one parameter.

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.

In this paper, we prove the existence of at least two weak solutions to a class of singular two-phase problems with variable exponents involving a ψ-Hilfer fractional operator and Dirichlet-type boundary conditions when the term source is dependent on one parameter. Here, we use the fiber method and the Nehari manifold to prove our results.

We consider the constrained nonlinear Schrödinger problem in $\mathbb{R}^{N}$ ($N\ge 3$) where $2< p,m<2+\tfrac{4}{N}$, $2^{*}=\tfrac{2N

In this paper, using variational methods introduced in the previous study on fractional elliptic systems, we prove the existence of at least three weak solutions for an elliptic nonlinear system with a p-Laplacian ψ-Hilfer operator.