Results 31 to 40 of about 59 (54)

The existence and boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms

Advances in Nonlinear Analysis, 2014
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
Zhang Zhijun
doaj   +1 more source

Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity

Advances in Nonlinear Analysis, 2018
We study the semilinear elliptic ...
Ghergu Marius, Kim Sunghan, Shahgholian Henrik   +2 more
doaj   +1 more source

Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions

Advances in Nonlinear Analysis
Let Ω⊂Rn\Omega \subset {{\bf{R}}}^{n} be a smooth bounded domain. In this article, we prove a result of which the following is a by-product: Let q∈]0,1[q\in ]0,1{[}, α∈L∞(Ω)\alpha \in {L}^{\infty }\left(\Omega ), with α>0\alpha \gt 0, and k∈Nk\in {\bf{N}}
Ricceri Biagio
doaj   +1 more source

Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity

Advances in Nonlinear Analysis, 2014
We study the following nonlinear Schrödinger equations: -Δu+V(x)u=f(u)inℝN.$ - \Delta u + V(x) u = f(u) \quad \text{in } {\mathbb {R}^N}. $ The purpose of this paper is to establish the existence of a positive solution under general conditions which are ...
Sato Yohei, Shibata Masataka
doaj   +1 more source

Infinitely many normalized solutions for Schrödinger equations with local sublinear nonlinearity

Demonstratio Mathematica
In this article, we investigate the following Schrödinger equation: −Δu=h(x)g(u)+λuinRN,∫RN∣u∣2dx=au∈H1(RN),\left\{\begin{array}{ll}-\Delta u=h\left(x)g\left(u)+\lambda u\hspace{1.0em}& \hspace{-0.2em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{
Xu Qin, Li Gui-Dong
doaj   +1 more source

Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates

Advanced Nonlinear Studies, 2020
We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained ...
Mancini Gabriele, Martinazzi Luca
doaj   +1 more source

Nonexistence of positive radial solutions for a problem with singular potential

Advances in Nonlinear Analysis, 2014
This article completes the picture in the study of positive radial solutions in the function space 𝒟1,2(ℝN)∩L2(ℝN,|x|-αdx)∩Lp(ℝN)${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the ...
Catrina Florin
doaj   +1 more source

Dirac-harmonic maps with potential. [PDF]

Lett Math Phys, 2022
Branding V.
europepmc   +1 more source

An upper bound for the least energy of a sign-changing solution to a zero mass problem

Advanced Nonlinear Studies
We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation −Δu=f(u),u∈D1,2(RN), $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\right),$ where N ≥ 5 and the nonlinearity f is
Clapp Mónica, Maia Liliane, Pellacci Benedetta   +2 more
doaj   +1 more source

Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

Advances in Nonlinear Analysis, 2018
Consider nonlinear Choquard ...
Seok Jinmyoung
doaj   +1 more source