Published in Advances in Nonlinear Analysis
We consider the following problem: given a bounded convex domain Ω⊂ℝ N ${\Omega \subset \mathbb {R}^N}$ we consider the limit as p → ∞ of solutions to -div(b p -p |Du| p-2 Du)=f + -f - ${- \operatorname{div} (b_{p}^{-p} |Du|^{p-2} Du)=f_+ - f_-}$ in Ω and b p -p |Du| p-2 ∂u ∂η=0${ b_{p}^{-p} |Du|^{p-2} \frac{\partial u}{\partial \eta }=0}$ on ∂Ω${\...
Published in Advances in Nonlinear Analysis
The paper deals with variational properties of fixed points for contraction-type operators. Under suitable conditions, the unique fixed point of a vector-valued operator is a Nash-type equilibrium of the corresponding energy functionals. This is achieved by an iterative scheme based on Ekeland's variational principle. An application to periodic sol...
Published in Advances in Nonlinear Analysis
We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein–Gordon equation. We also establish a linear instability criterium for a KdV type system. An application of this approach is made to obtain the linear/nonlinear instability of vector cnoidal wave profiles. Finally, via a theor...
Published in Advances in Nonlinear Analysis
This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions on the matter field and nonhomogeneous Neumann boundary conditions on the electric potential. Un...
Published in Advances in Nonlinear Analysis
In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δ ℍ n u=μg(ξ)u (|z| 4 +t 2 ) 1 2 +λf(ξ,u)$-\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...
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$...
Published in Advances in Nonlinear Analysis
In this paper, for more general f, g and a, b, we obtain conditions about the existence and boundary behavior of solutions to boundary blow-up elliptic problems ▵u=a(x)g(u)+b(x)f(u)|∇u| q ,x∈Ω,u| ∂Ω =+∞$ \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...
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
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...
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...
