Results 91 to 100 of about 1,290,485 (220)
Higher order energy expansions for some singularly perturbed Neumann problems [PDF]
, 2003 We consider the following singularly perturbed semilinear elliptic problem: \epsilon^{2} \Delta u - u + u^p=0 \ \ \mbox{in} \ \Omega, \quad u>0 \ \ \mbox{in} \ \ \Omega \quad \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \
Winter, M +5 more
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Nonexistence results for solutions of semilinear elliptic equations
Duke Mathematical Journal, 1994 Consider the semilinear elliptic equation (1) \(\Delta u= f(| x|)u+ g(x) u^ q\), \(x\in \mathbb{R}_ 0^ N\) for \(N\geq 3\), \(q>1\), where \(\mathbb{R}_ 0^ N= \mathbb{R}^ N\setminus \{0\}\), \(f\in L^ 1_{\text{loc}} (\mathbb{R}_ 0^ +)\), \(g\in L^ \infty_{\text{loc}} (\mathbb{R}_ 0^ N)\), \(g\geq 0\). The main theorems are sufficient conditions on \(f\)
BENGURIA, RD, LORCA, S, YARUR, CS
openaire +3 more sources
Semilinear elliptic partial differential equations with the critical Sobolev exponent [PDF]
, 2017 We present how variational methods and results from linear and non-linear functional analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs).
Mavuso, Melusi Manqoba
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Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one
Electronic Journal of Differential Equations, 2006 In this article, we consider a semilinear elliptic equations of the form $Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$.
Janos Englander, Peter L. Simon
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Inhomogeneous parabolic equations on unbounded metric measure spaces [PDF]
, 2012 We study the inhomogeneous semilinear parabolic equation ut = Δu + up + f(x), with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type
Hu, Jiaxin +6 more
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Dimension of the set of positive solutions to nonlinear equations and applications
Electronic Journal of Differential Equations, 2016 We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness ...
Petronije S. Milojevic
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Harnack inequality for non-divergence structure semi-linear elliptic equations
Advances in Nonlinear Analysis, 2018 In this paper we establish a Harnack inequality for non-negative solutions of Lu=f(u){Lu=f(u)} where L is a non-divergence structure uniformly elliptic operator and f is a non-decreasing function that satisfies an appropriate growth conditions at ...
Mohammed Ahmed, Porru Giovanni
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On the solution stability of parabolic optimal control problems. [PDF]
Comput Optim Appl, 2023 Corella AD, Jork N, Veliov VM.
europepmc +1 more source
, 1996 We peove various results concerning a priori bounds of positive solutions of higher order equations and semilinear elliptic ...
CLEMENT PH +2 more
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Electronic Journal of Differential Equations, 2015 This article shows the existence of solutions by the least action principle, for semilinear elliptic equations with Neumann boundary conditions, under critical growth and local coercive conditions.
Qin Jiang, Sheng Ma
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