Results 21 to 30 of about 551 (71)

Flat solutions of the 1-Laplacian equation [PDF]

, 2017
For every $f \in L^N(\Omega)$ defined in an open bounded subset $\Omega$ of $\mathbb{R}^N$, we prove that a solution $u \in W_0^{1, 1}(\Omega)$ of the $1$-Laplacian equation ${-}\mathrm{div}{(\frac{\nabla u}{|\nabla u|})} = f$ in $\Omega$ satisfies ...
Orsina, Luigi, Ponce, Augusto C.
core   +3 more sources

Positive Solutions for Resonant (p, q)-equations with convection

Advances in Nonlinear Analysis, 2020
We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift
Liu Zhenhai, Papageorgiou Nikolaos S.
doaj   +1 more source

Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries

Advanced Nonlinear Studies, 2023
In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating (N+1)\left(N+1)-dimensional thin domains (i.e., a family of bounded open sets from RN+1{{\mathbb{R}}}^{N+1}, with corrugated bounder ...
Nakasato Jean Carlos, Pereira Marcone Corrêa   +1 more
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N-Laplacian critical problem with discontinuous nonlinearities

Advances in Nonlinear Analysis, 2015
In this paper, we study the existence of a solution of the N-Laplacian critical problem with discontinuous nonlinearity of Heaviside type in a smooth bounded domain with respect to a positive parameter λ.
Tiwari Sweta
doaj   +1 more source

A bifurcation result involving Sobolev trace embedding and the duality mapping of W1,p

Moroccan Journal of Pure and Applied Analysis, 2017
We consider the perturbed nonlinear boundary condition ...
El Khalil Abdelouahed
doaj   +1 more source

Continuity results for parametric nonlinear singular Dirichlet problems

Advances in Nonlinear Analysis, 2019
In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameter λ > 0 that was considered in [32].
Bai Yunru, Motreanu Dumitru, Zeng Shengda   +2 more
doaj   +1 more source

A Picone identity for variable exponent operators and applications

Advances in Nonlinear Analysis, 2019
In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u).
Arora Rakesh, Giacomoni Jacques, Warnault Guillaume   +2 more
doaj   +1 more source

An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

, 2020
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes.
Della Pietra, Francesco, Piscitelli, Gianpaolo   +1 more
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On viscosity and weak solutions for non-homogeneous p-Laplace equations

Advances in Nonlinear Analysis, 2017
In this manuscript, we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower-order term depending on x, u and ∇⁡u{\nabla u}.
Medina Maria, Ochoa Pablo
doaj   +1 more source

Supersolutions to nonautonomous Choquard equations in general domains

Advances in Nonlinear Analysis, 2023
We consider the nonlocal quasilinear elliptic problem: −Δmu(x)=H(x)((Iα*(Qf(u)))(x))βg(u(x))inΩ,-{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }* \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0 ...
Aghajani Asadollah, Kinnunen Juha
doaj   +1 more source