Results 31 to 40 of about 369 (47)

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
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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

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
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Solutions of vectorial Hamilton–Jacobi equations are rank-one absolute minimisers in L∞L^{\infty}

Advances in Nonlinear Analysis, 2017
Given the supremal functional E∞⁢(u,Ω′)=ess⁢supΩ′⁡H⁢(⋅,D⁢u){E_{\infty}(u,\Omega^{\prime})=\operatornamewithlimits{ess\,sup}_{\Omega^{% \prime}}H(\,\cdot\,,\mathrm{D}u)}, defined on Wloc1,∞⁢(Ω,ℝN){W^{1,\infty}_{\mathrm{loc}}(\Omega,\mathbb{R}^{N})}, with ...
Katzourakis Nikos
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A boundary regularity result for minimizers of variational integrals with nonstandard growth

, 2018
We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example ...
Bulíček, Miroslav, Maringová, Erika, Stroffolini, Bianca, Verde, Anna   +3 more
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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
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On the well-posedness of global fully nonlinear first order elliptic systems

Advances in Nonlinear Analysis, 2018
In the very recent paper [15], the second author proved that for any f∈L2⁢(ℝn,ℝN){f\in L^{2}(\mathbb{R}^{n},\mathbb{R}^{N})}, the fully nonlinear first order system F⁢(⋅,D⁢u)=f{F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L.
Abugirda Hussien, Katzourakis Nikos
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Nonoccurrence of Lavrentiev gap for a class of functionals with nonstandard growth

Advances in Nonlinear Analysis
We consider the functional ℱ(u)≔∫Ωf(x,Du(x))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }f\left(x,Du\left(x)){\rm{d}}x, where f(x,z)f\left(x,z) satisfies a (p,q)\left(p,q)-growth condition with respect to zz and can be ...
De Filippis Filomena, Leonetti Francesco, Treu Giulia   +2 more
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The fibering method approach for a Schrödinger-Poisson system with p-Laplacian in bounded domains

Open Mathematics
In this article, we study a p-Laplacian Schrödinger-Poisson system involving a parameter q≠0q\ne 0 in bounded domains. By using the Nehari manifold and the fibering method, we obtain the non-existence and multiplicity of nontrivial solutions. On one hand,
Xue Jinfeng, Wang Libo
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k-convex solutions for multiparameter Dirichlet systems with k-Hessian operator and Lane-Emden type nonlinearities

Advances in Nonlinear Analysis
In this article, our main aim is to investigate the existence of radial kk-convex solutions for the following Dirichlet system with kk-Hessian operators: Sk(D2u)=λ1ν1(∣x∣)(−u)p1(−v)q1inℬ(R),Sk(D2v)=λ2ν2(∣x∣)(−u)p2(−v)q2inℬ(R),u=v=0on∂ℬ(R).\left\{\begin ...
He Xingyue, Gao Chenghua, Wang Jingjing
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