Results 21 to 30 of about 383 (68)

Bounded solutions for a class of Hamiltonian systems

, 2017
We obtain bounded for all $t$ solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on $(-L,L)$, with $L \rightarrow \infty$.
Korman, Philip, Peng, Guanying
core   +1 more source

Duality methods for a class of quasilinear systems

, 2013
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially different forms ...
Agarwal, Albujer, Alías, Antonella Marini, Edelen, Iwaniec, Lee, Magnanini, Magnanini, Marini, Marini, Milani, Morrey, Otway, Otway, Otway, Schwarz, Sibner, Sibner, Sibner, Thomas H. Otway, Yang   +21 more
core   +1 more source

Regularity of minimizers for double phase functionals of borderline case with variable exponents

Advances in Nonlinear Analysis
The aim of this article is to study regularity properties of a local minimizer of a double phase functional of type ℱ(u)≔∫Ω(∣Du∣p(x)+a(x)∣Du∣p(x)log(e+∣Du∣))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }({| Du| }^{p\left(x)}+a ...
Ragusa Maria Alessandra, Tachikawa Atsushi   +1 more
doaj   +1 more source

Existence via regularity of solutions for elliptic systems and saddle points of functionals of the calculus of variations

Advances in Nonlinear Analysis, 2017
The core of this paper concerns the existence (via regularity) of weak solutions in W01,2${W_{0}^{1,2}}$ of a class of elliptic systems such ...
Boccardo Lucio, Orsina Luigi
doaj   +1 more source

A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient

Advanced Nonlinear Studies, 2020
We consider the elliptic equation -Δ⁢u=uq⁢|∇⁡u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta, Pucci Patrizia, Souplet Philippe   +2 more
doaj   +1 more source

Existence of positive radial solutions of general quasilinear elliptic systems

Advances in Nonlinear Analysis
Let Ω⊂Rn(n≥2)\Omega \subset {{\mathbb{R}}}^{n}\hspace{0.33em}\left(n\ge 2) be either an open ball BR{B}_{R} centred at the origin or the whole space. We study the existence of positive, radial solutions of quasilinear elliptic systems of the form Δpu=f1(∣
Devine Daniel
doaj   +1 more source

Boundedness, existence and uniqueness results for coupled gradient dependent elliptic systems with nonlinear boundary condition

Advances in Nonlinear Analysis
In this paper, we study coupled elliptic systems with gradient dependent right-hand sides and nonlinear boundary conditions, where the left-hand sides are driven by so-called double phase operators.
Frisch Michal Maria, Winkert Patrick
doaj   +1 more source

Groundstates of the Choquard equations with a sign-changing self-interaction potential

, 2018
We consider a nonlinear Choquard equation $$ -\Delta u+u= (V * |u|^p )|u|^{p-2}u \qquad \text{in }\mathbb{R}^N, $$ when the self-interaction potential $V$ is unbounded from below.
Battaglia, Luca, Van Schaftingen, Jean
core   +1 more source

Ground State for a Coupled Elliptic System with Critical Growth

Advanced Nonlinear Studies, 2018
We study the following coupled elliptic system with critical nonlinearities:
Wu Huiling, Li Yongqing
doaj   +1 more source

Multiplicity of solutions for a nonhomogeneous quasilinear elliptic equation with concave-convex nonlinearities

Advances in Nonlinear Analysis
We investigate the multiplicity of solutions for a quasilinear scalar field equation with a nonhomogeneous differential operator defined bySu≔−divϕu2+∣∇u∣22∇u+ϕu2+∣∇u∣22u,Su:= -\hspace{0.1em}\text{div}\hspace{0.1em}\left\{\phi \left(\frac{{u}^{2 ...
Qi Wanting, Zhang Xingyong
doaj   +1 more source