We are interested in the multiplicity of weak solutions for a binonlocal fractional $p(x,\cdot )$-Kirchhoff type problems. Our technical approach is based on the general three critical points theorem obtained by B. Ricceri.

This work is devoted to the study of a class of nonlocal impulsive integrodifferential equations of Volterra type. We investigate the situation when the resolvent operator corresponding to the linear part of

is norm continuous. Our results are obtained by using the Hausdorff measure of noncompactness and fixed point theorems. An example is provided to illustrate the basic theory of this work.

This paper is devoted to the study of the solvability of a class of integral equations, whose kernel depends on four different functions. To obtain necessary and sufficient conditions for the unique solution of this class of equations, we introduce eight new weighted convolutions associated with the kernel of our equations. Moreover, we obtain two Young-type inequalities associated with each convolution.

We introduce the concept of a convex-power condensing mapping $A\cdot B+C$ in a Banach algebra relative to a measure of noncompactness as a generalization of condensing and convex-power condensing mappings. We present new fixed point theorems, and we apply these results to investigate the existence of solutions for a nonlinear hybrid integral equation of Volterra type.

In this paper we study an abstract class of weakly dissipative Moore–Gibson–Thompson equation with finite memory. We establish a general decay rate for the solution of the system under some appropriate conditions on the relaxation function.

This paper is devoted to scrutinizing the existence and uniqueness of mild solutions to a hybrid fractional differential equations subject to state-dependent nonlocal conditions. Special cases of the considered class and the formulated theorems will be displayed. Some examples will be given to illustrate the main results.

While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be missing. Moreover, the available formula contains an integral term including the time derivative of the fundamental solution of the heat equation, whose interpretation is difficult at second glance. To fill these gaps, we provide a rigorous proof of a general version of the integration by parts formula and an alternative representation of the mentioned integral term, which is valid for a certain class of functions including the typical tensor-product discretization spaces.