One Citation
Existence, multiplicity and classification results for solutions to $k$-Hessian equations with general weights
- Mathematics
- 2022
The aim of this paper is to study negative classical solutions to a k -Hessian equation involving a nonlinearity with a general weight Here, B denotes the unit ball in R n , n > 2 k ( k ∈ N ), λ is a…
References
SHOWING 1-10 OF 43 REFERENCES
Singular Solutions of Elliptic Equations with Iterated Exponentials
- MathematicsThe Journal of Geometric Analysis
- 2019
We construct positive singular solutions for the problem $$-\Delta u=\lambda \exp (e^u)$$ - Δ u = λ exp ( e u ) in $$B_1\subset {\mathbb {R}}^n$$ B 1 ⊂ R n ( $$n\ge 3$$ n ≥ 3 ), $$u=0$$ u = 0 on…
A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth
- Mathematics
- 2018
A generalized Pohozaev identity and its applications
- Mathematics
- 1990
in $R^{n}$ , where $Du$ is the gradient of $u,$ $f(|x|, u)$ and $A(p)$ are given functions. The Pohozaev identity is useful to investigate the existence and non-existence of the ground state of…
Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball
- Mathematics
- 2015
Let $$B\subset \mathbb {R}^N$$B⊂RN, $$N\ge 3$$N≥3, be the unit ball. We study the global bifurcation diagram of the solutions of $$\begin{aligned} {\left\{ \begin{array}{ll} \Delta u+\lambda f(u)=0…
A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions
- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2017
We consider the following semilinear elliptic equation: where B 1 is the unit ball in ℝ d , d ≥ 3, λ > 0 and p > 0. Firstly, following Merle and Peletier, we show that there exists an eigenvalue λ…
The Liouville–Bratu–Gelfand Problem for Radial Operators
- Mathematics
- 2002
Abstract We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes…
Intersection properties for singular radial solutions of quasilinear elliptic equations with Hardy type potentials
- MathematicsComplex Variables and Elliptic Equations
- 2021
Some Positone Problems Suggested by Nonlinear Heat Generation
- Mathematics
- 1967
There is much current interest in boundary value problems containing positive linear differential operators and monotone functions of the dependent variable, see for example, M.A. Krasnosel'ski [1]…
Radial single point rupture solutions for a general MEMS model
- MathematicsCalculus of Variations and Partial Differential Equations
- 2022
We study the initial value problem $$ \begin{cases} r^{-(\gamma-1)}\left(r^{\alpha}|u'|^{\beta-1}u'\right)'=\frac{1}{f(u)} & \textrm{for}\ 0 0 & \textrm{for}\ 0 \alpha>\beta\geq 1$ and $f\in C[0,\bar…
Stable solutions to semilinear elliptic equations are smooth up to dimension $9$
- MathematicsActa Mathematica
- 2020
In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension $n \leq 9$.
This result, that was only…