Results 91 to 100 of about 160 (129)

Existence of solutions for a class of quasilinear Schrödinger equations with Choquard-type nonlinearity

Advances in Nonlinear Analysis
For the following quasilinear Choquard-type equation: −Δu−Δ(u2)u+V(x)u=(Iμ*∣u∣p)∣u∣p−2u,x∈RN,-\Delta u-\Delta \left({u}^{2})u+V\left(x)u=\left({I}_{\mu }* {| u| }^{p}){| u| }^{p-2}u,\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N≥3 ...
Shen Zifei, Yang Ning
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On the existence of a priori bounds for positive solutions of elliptic problems, I

Revista Integración, 2019
This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations (P)p     -\Delta_p u =f(u),  in  \Omega,    u = 0, on \partial\Omega widening the known ranges of subcritical ...
Rosa Pardo
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Multiple positive solutions for superlinear Kirchhoff type problems on R^N

Electronic Journal of Differential Equations, 2015
In this article, we study the multiplicity of positive solutions for a class of Kirchhoff type problems depending on two real functions and a nonnegative parameter on an unbounded domain.
Yu Duan, Chun-Lei Tang
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Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth

Electronic Journal of Differential Equations, 2017
This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial.
Hua Jin, Wenbin Liu
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Pohozaev-like identity for the regional fractional laplacian

We establish a new integration by parts formula for the regional fractional laplacian $(-Δ)^s_Ω$ in bounded open sets of class $C^2$. As a direct application, we prove that weak solutions to the corresponding Dirichlet problem satisfy a Pohozaev-like identity with an explicit remainder term.
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Infinitely many radial solutions for a sub-super critical Dirichlet boundary value problem in a ball

Electronic Journal of Differential Equations, 2007
We prove the existence of infinitely many solutions to a semilinear Dirichlet boundary value problem in a ball for a nonlinearity $g(u)$ that grows subcritically for $u$ positive and supercritically for $u$ negative.
Chee Meng Tan, John Kwon, Alfonso Castro
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Nonexistence results for semilinear systems in unbounded domains

Electronic Journal of Differential Equations, 2009
This paper concerns the non-existence of nontrivial solutions for the semi-linear system of gradient type $$displaylines{ lambda frac{partial ^{2}u_{k}}{partial t^{2}} -sum_{i=1}^n frac{partial }{partial x_{i}}(p_{i}(x)frac{ partial u_{k}}{partial x_{i}}
Abdelkrim Moussaoui, Brahim Khodja
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The Stress-Energy Tensor and Pohozaev's Identity for Systems

, 2012
Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev's identity for certain classes of quasilinear systems with variational structure. © 2012 Wuhan Institute of Physics and Mathematics.
Alikakos, N.D., Faliagas, A.C.
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Regular solutions to elliptic equations

Electronic Journal of Differential Equations, 2023
Alfonso Castro, Jon Jacobsen
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Pohozaev identity and its applications

Pohozaev identity and its applications
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