Catrina, Florin
Published in
Advances in Nonlinear Analysis

This article completes the picture in the study of positive radial solutions in the function space 𝒟 1,2 (ℝ N )∩L 2 (ℝ N ,|x| -α dx)∩L p (ℝ N )${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the equation -Δu+A |x| α u=u p-1 inℝ N ∖{0}withN≥3,A>0,α>0,p>2.$- \Delta u + \frac{A}{|...

Erhardt, André
Published in
Advances in Nonlinear Analysis

We establish local Calderón–Zygmund estimates for solutions to certain parabolic problems with irregular obstacles and nonstandard p(x,t)${p(x,t)}$ -growth. More precisely, we will show that the spatial gradient Du${Du}$ of the solution to the obstacle problem is as integrable as the obstacle ψ${\psi }$ , i.e. |Dψ| p(·) ,|∂ t ψ| γ 1 ' ∈L loc q ⇒|Du...

Bonanno, Claudio
Published in
Advances in Nonlinear Analysis

In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and charge. In particular we show that under mild assumptions on the nonlinear term it is possible to prove the exist...

Beirão da Veiga, Hugo
Published in
Advances in Nonlinear Analysis

We turn back to some pioneering results concerning, in particular, nonlinear potential theory and non-homogeneous boundary value problems for the so-called p-Laplace operator. Unfortunately these results, obtained at the very beginning of the seventies, were kept in the shade. We believe that our proofs are still of interest, in particular due to t...

Ignatova, Mihaela
Published in
Advances in Nonlinear Analysis

We address the regularity of solutions to elliptic and parabolic equations of the form -Δu+b·∇u=0${- \Delta u+b\cdot \nabla u=0}$ and u t -Δu+b·∇u=0${u_t- \Delta u+b\cdot \nabla u=0}$ with divergence-free drifts b. We are particularly interested in the case when the drift velocity b is assumed to be at the supercritical regularity level with respec...

Alleche, Boualem
Published in
Advances in Nonlinear Analysis

This paper deals with solving equilibrium problems under local conditions on equilibrium bifunctions. Some techniques first considered for multivalued mixed variational inequalities are investigated and applied to equilibrium problems. It results that the notion of hemicontinuity is not needed on the whole space when solving equilibrium problems in...

Manna, Bhakti B. Srikanth, P. Chakravarthy
Published in
Advances in Nonlinear Analysis

Let A={x∈ℝ 2N+2 :0 0 in A, ∂u ∂ν=0$\frac{\partial u}{\partial \nu } = 0$ on ∂A$\partial A$ , where 1

Zhang, Zhijun
Published in
Advances in Nonlinear Analysis

In this paper, for more general f, g and a, b, we obtain conditions about the existence and boundary behavior of solutions to boundary blow-up elliptic problems ▵u=a(x)g(u)+b(x)f(u)|∇u| q ,x∈Ω,u| ∂Ω =+∞$ \triangle u=a(x)g(u)+ b(x) f(u)|\nabla u|^q,\quad x\in \Omega ,\quad u|_{\partial \Omega }=+\infty $ and improve and generalize most of the previo...

Kurta, Vasilii V.
Published in
Advances in Nonlinear Analysis

We obtain a new Liouville comparison principle for weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form u t -ℒu-|u| q-1 u≥v t -ℒv-|v| q-1 v(*)$u_t -{\mathcal {L}}u- |u|^{q-1}u\ge v_t -{\mathcal {L}}v- |v|^{q-1}v\qquad (*)$ in the whole space ℝ×ℝ n ${{\mathbb {R}} \times \mathbb {R}^n}$ . Here, n≥1$...

Tyagi, Jagmohan
Published in
Advances in Nonlinear Analysis

In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δ ℍ n u=μg(ξ)u (|z| 4 +t 2 ) 1 2 +λf(ξ,u)$-\Delta _{{\mathbb {H}}^{n}} u= \mu \frac{g(\xi ) u}{(|z|^{4}+ t^{2} )^{\frac{1}{2} }} +\lambda f(\xi , u)$ in Ω, u=0$ u =0$ on ∂Ω$\partial \Omega $ on the Heisenberg group. We employ Bonanno's three...