Singular solutions to $k$-Hessian equations with fast-growing nonlinearities

  title={Singular solutions to \$k\$-Hessian equations with fast-growing nonlinearities},
  author={'O JoaoMarcosdo and Evelina Shamarova and Esteban da Silva},
1 Citations
Existence, multiplicity and classification results for solutions to $k$-Hessian equations with general weights
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


Singular Solutions of Elliptic Equations with Iterated Exponentials
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 generalized Pohozaev identity and its applications
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Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball
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A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions
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
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
Some Positone Problems Suggested by Nonlinear Heat Generation
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
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 $9$
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