ABSTRACT: In the present paper, an elliptic equation with Hardy-Sobolev critical exponent, Hardy-Sobolev-Maz’ya potential and sign-changing weights, is considered. By using the Nehari manifold and ...

Mathematical chaos has a variety of definitions. The definition given by Strogatz states: Chaos is aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial ...

ABSTRACT: In this paper, we establish the existence of at least four distinct solutions to an elliptic problem with singular cylindrical potential, a concave term, and critical ...

Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

Abstract: Two different equations, both of which are often called ‘the Cole–Cole equation’, are widely used to fit experimental Spectral Induced Polarization data. The data are compared on the basis ...

Abstract: In different areas like physics, engineering, biology, for example, to predict the behavior of composite systems one has to solve complex differential equations. This paper reviews the ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...