This paper aims to investigate a type of nonlinear elliptic equation that contains a Hardy potential, lower order term and (L^{m(.)}) datum in the setting of Sobolev spaces with variable exponent. Despite the presence of a Hardy potential, the existence of solutions and regularizing effect of some lower order terms in (p(x)-)Laplacian type elliptic equations are proved.
In this sequel paper, we continue our study on co-maximal subgroup graph (Gamma (G)) of a group G. We discuss some further results on connectedness and when (Gamma (G)) is edgeless. Moreover, we study the independence number, chromatic number and perfectness of (Gamma (G)). In the process, we show that if the independence number is suitably small, then the underlying group is solvable. We also classify co-maximal subgroup graphs of certain groups upto isomorphism.
In this paper, we consider finite groups with few kernels of nonlinear irreducible characters and classify finite solvable groups with two kernels of nonlinear irreducible characters. Nonsolvable groups with this property are also investigated.
By using Monte Carlo simulations of the Wigner–Boltzmann transport equation, the validity of a smooth quantum hydrodynamic model has been investigated in a GaAs Resonant Tunneling Diode. The common approximation of the heat flux by Fourier’s law is shown to differ substantially from the actual heat flux.
In this paper, we prove that if two finite groups G and H have isomorphic Burnside rings, then G and H are the same order type groups, and give an example to show that the Burnside rings of the same order type groups are not necessarily isomorphic. This result is related to the Thompson Problem which was raised in 1987.
This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we mainly proved that the weak solution is regular on (0, T] provided that either the norm (left| pi right| _{L^{alpha ,infty }(0,T;L^{beta ,infty }(mathbb {R}^{3}))}) with (frac{2}{alpha }+ frac{3}{beta }=2) and (frac{3}{2}<beta <infty ) or (left| nabla pi right| _{L^{alpha ,infty }(0,T;L^{beta ,infty }(mathbb {R} ^{3}))}) with (frac{2}{alpha }+frac{3}{beta }=3) and (1<beta <infty ) is sufficiently small.
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