The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.

We extend several known results on solvability in the Sobolev spaces W 1 p , p ∈ [2,∞), of SPDEs in divergence form in R d + to equations having coefficients which are discontinuous in the space variable.

The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...

We study quasi–Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of ε depends on ε−1 and the dimension s. Strong tractability means that it does not depend on s and is bounded by a polynomial in ε−1. The least po...

We consider an inverse problem of recovering the non-linearity in one dimensional variable exponent $p(x)$-Laplace equation from Dirichlet-to-Neumann map. The can be recovered up to natural obstruction rearrangements. main technique is using a Muntz-Szasz theorem after reducing determining function its $L^p$-norms.

In this paper we deal with the Cauchy problem for evolution equations with real characteristics. We show that the problem is well-posed in Sobolev spaces assuming a suitable decay of the coefficients as the space variable x → ∞. In some cases, such a decay may also compensate a lack of regularity with respect to the time variable t.

We consider the regularity of solutions for some parabolic equations. We show Hölder continuity with exponent (1 + α)/2, with respect to the time variable, when the gradient in the space variable of the solution has the Hölder continuity with exponent α.

where a ( x ) is a given function on M . The original interest in such questions grew out of Yamabe's problem (see [40], [39], [2], [27], [15]) which corresponds to the special case where a ( x ) = ( ( N 2)/4(N l ) ) R ( x ) and R ( x ) is the scalar curvature of M . It turns out that, despite its simple form, equation (1) (or ( 2 ) ) has a very rich structure and provides an amazing source of ...

Via the variational methods, we prove the existence of a nontrivial solution to a singular semilinear elliptic equation with critical Sobolev-Hardy exponent under certain conditions .