scholarly journals Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential

2010 ◽  
Vol 225 (6) ◽  
pp. 2967-3021 ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Ireneo Peral ◽  
Ana Primo
Keyword(s):  
Critical Growth ◽  
Physical Models ◽  
Parabolic Problems ◽  
Hardy Potential

scholarly journals Fractional KPZ equations with critical growth in the gradient respect to Hardy potential

2020 ◽  
Vol 201 ◽  
pp. 111942
Author(s):  
Boumediene Abdellaoui ◽  
Ireneo Peral ◽  
Ana Primo ◽  
Fernando Soria
Keyword(s):  
Critical Growth ◽  
Hardy Potential

scholarly journals MULTIPLE POSITIVE SOLUTIONS FOR A CRITICAL GROWTH PROBLEM WITH HARDY POTENTIAL

2006 ◽  
Vol 49 (1) ◽  
pp. 53-69 ◽  
Author(s):  
Pigong Han
Keyword(s):  
Dirichlet Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Variational Approach ◽  
Critical Growth ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Unique Positive Solution ◽  
Existence And Nonexistence ◽  
Growth Problem

AbstractIn this paper we study the existence and nonexistence of multiple positive solutions for the Dirichlet problem:$$ -\Delta{u}-\mu\frac{u}{|x|^2}=\lambda(1+u)^p,\quad u\gt0,\quad u\in H^1_0(\varOmega), \tag{*} $$where $0\leq\mu\lt(\frac{1}{2}(N-2))^2$, $\lambda\gt0$, $1\ltp\leq(N+2)/(N-2)$, $N\geq3$. Using the sub–supersolution method and the variational approach, we prove that there exists a positive number $\lambda^*$ such that problem (*) possesses at least two positive solutions if $\lambda\in(0,\lambda^*)$, a unique positive solution if $\lambda=\lambda^*$, and no positive solution if $\lambda\in(\lambda^*,\infty)$.

Nonlinear parabolic problems with critical growth and unbounded data

2001 ◽  
Vol 50 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Vincenzo Ferone ◽  
Maria Rosasia Posteraro ◽  
Jean Michel Rakotoson
Keyword(s):  
Critical Growth ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic

scholarly journals FOUNTAIN-LIKE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH CRITICAL GROWTH AND HARDY POTENTIAL

2005 ◽  
Vol 07 (06) ◽  
pp. 867-904 ◽  
Author(s):  
VERONICA FELLI ◽  
SUSANNA TERRACINI
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Blow Up ◽  
Nonlinear Elliptic Equations ◽  
Critical Growth ◽  
Hardy Potential ◽  
Nonlinear Elliptic ◽  
Hardy Type ◽  
Type Potential

We prove the existence of fountain-like solutions, obtained by superposition of bubbles of different blow-up orders, for a nonlinear elliptic equation with critical growth and Hardy-type potential.

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

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