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Positive Radial Solutions for a Class of Semilinear Elliptic Problems Involving Critical Hardy-Sobolev Exponent and Hardy Terms  [PDF]
Yong-Yi Lan
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.511180
Abstract: In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.
Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$  [PDF]
Salvador Villegas
Mathematics , 2009,
Abstract: We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation $-\Delta u=f(u)$ in the whole $R^N$, where $f\in C^1(R)$ is a general nonlinearity and $N\geq 1$ is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.
Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains
Peng Feng,Zhengfang Zhou
Electronic Journal of Differential Equations , 2005,
Abstract: The use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical system (MEMS) and in nanoelectromechanical systems (NEMS). Here, we study the electrostatic deflection of an annular elastic membrane. We investigate the exact number of positive radial solutions and non-radially symmetric bifurcation for the model $$ -Delta u=frac{lambda}{(1-u)^2}quadhbox{in }Omega, quad u=0 quadhbox{on }partial Omega, $$ where $Omega={xin mathbb{R}^2: epsilon<|x|<1}$. The exact number of positive radial solutions maybe 0, 1, or 2 depending on $lambda$. It will be shown that the upper branch of radial solutions has non-radially symmetric bifurcation at infinitely many $lambda_Nin (0,lambda^*)$. The proof of the multiplicity result relies on the characterization of the shape of the time-map. The proof of the bifurcation result relies on a well-known theorem due to Kielhofer.
Nonexistence of distributional supersolutions of a semilinear elliptic equation with Hardy potential  [PDF]
Mouhamed Moustapha Fall
Mathematics , 2011,
Abstract: In this paper we study nonexistence of non-negative distributional supersolutions for a class of semilinear elliptic equations involving inverse-square potentials.
Nonexistence of radial positive solutions for a nonpositone problem
Said Hakimi,Abderrahim Zertiti
Electronic Journal of Differential Equations , 2011,
Abstract: In this article we study the nonexistence of radial positive solutions for a nonpositone problem when the nonliearity is superlinear and has more than one zero.
Positive and oscillatory radial solutions of semilinear elliptic equations  [cached]
Shaohua Chen,William R. Derrick,Joseph A. Cima
International Journal of Stochastic Analysis , 1997, DOI: 10.1155/s1048953397000105
Abstract: We prove that the nonlinear partial differential equation Δu+f(u)+g(|x|,u)=0, in n,n≥3, with u(0)>0, where f and g are continuous, f(u)>0 and g(|x|,u)>0 for u>0, and limu→0+f(u)uq=B>0, for 1
Existence and Nonexistence of Positive Solutions for Quasilinear Elliptic Problem
K. Saoudi
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/275748
Abstract: Using variational arguments we prove some existence and nonexistence results for positive solutions of a class of elliptic boundary-value problems involving the -Laplacian.
Nonexistence of positive singular solutions for a class of semilinear elliptic systems  [cached]
Cecilia S. Yarur
Electronic Journal of Differential Equations , 1996,
Abstract: sub-solutions to $$left. eqalign{ Delta u =& a(x) v^p cr Delta v =& b(x) u^q cr} ight} { m in } Omega subset Bbb R^N,quad Nge 3,, $$ where $pgeq 1$, $qgeq 1$, $pq>1$, and $a$ and $b$ are nonnegative functions. As a consequence of this work, we obtain new results for biharmonic equations.
Existence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in $\rz^N$  [PDF]
Matthias Schneider
Mathematics , 2002,
Abstract: Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u - \lambda V(x) u = h(x) u^{p-1}$ for $2
Nonexistence of radial positive solutions for a nonpositone system in an annulus
Said Hakimi
Electronic Journal of Differential Equations , 2011,
Abstract: In this article we study the nonexistence of radial positive solutions for a nonpositone system in an annulus by using energy analysis and comparison methods.
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