In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

We consider the exponential reaction–diffusion equation in space-dimension n ∈ (2, 10). We show that for any integer k ≥ 2 there is a backward selfsimilar solution which crosses the singular steady state k-times. The sameholds for the power nonlinearity if the exponent is supercritical in the Sobolev sense and subcritical in the Joseph–Lundgren sense. © 2008 Elsevier Ltd. All rights reserved.

In this paper we prove an existence and uniqueness result for the double phase Dirichlet problem when lowest exponent is equal to 1. Our solution a function of bounded variation that simultaneously lies in suitable weighted Sobolev space found as limit sequence solutions intermediate problems whose $p$ goes As that, our approach involves study some relevant properties generalized Orlicz-Sobolev...

We study multivariate integration in the worst case setting and multivariate approximation in the average case setting for various classes of functions of d variables with arbitrary d. We consider algorithms that use function evaluations as the information about the function. We are mainly interested in checking when integration and approximation are tractable and strongly tractable. Tractabili...

This paper deals with Strauss and Lions-type theorems for fractional Sobolev spaces variable exponent $$W^{s,p(.),{\tilde{p}}(.,.)} (\Omega )$$ , when p $${\tilde{p}}$$ satisfy some conditions. As application, we study the existence of solutions a class Kirchhoff–Choquard problem in $${\mathbb {R}}^N$$ .

Let Ω be a bounded smooth domain in R with N ≥ 2 and 1 < p < ∞. We denote by p∗ the critical exponent for the Sobolev trace immersion given by p∗ = p(N − 1)/(N − p) if p < N and p∗ = ∞ if p ≥ N . For any A ⊂ Ω, which is a smooth open subset, we define the space W 1,p A (Ω) = C ∞ 0 (Ω \A), where the closure is taken in W −norm. By the Sobolev Trace Theorem, there is a compact embedding (1.1) W 1...

In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties corresponding Musielak-Orlicz Sobolev spaces (an equivalent norm, uniform convexity, Radon-Riesz property respect to modular) and (continuity, strict monotonicity, (S+)-property). contrast known constant exponent case are abl...