we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

We present an improved version of an earlier Larson-type model of amphiphiles. Detailed descriptions of the algorithms are given and some situations where care must be taken are pointed out We use the model to calculate the condensation transition temperature of amphiphiles in a ternary mixture. The concentration percolation threshold and percolation critical exponent of arnphiphile clusters at...

This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of convolution type nonlinearity tends critical one in sense Hardy–Littlewood–Sobolev inequality, we obtain existence multiple positive solutions via Lusternik–Schnirelmann category and nonlocal global compactness. Moreover, prove that topology domain furnishes ...

‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.