نتایج جستجو برای: semilinear elliptic problem

تعداد نتایج: 908554  

Journal: :Analysis & PDE 2022

We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or some unbounded domains.

2009
Jean Dolbeault

Non-existence and uniqueness results are proved for several local and non-local supercritical bifurcation problems involving a semilinear elliptic equation depending on a parameter. The domain is star-shaped and such that a Poincaré inequality holds but no other symmetry assumption is required. Uniqueness holds when the bifurcation parameter is in a certain range. Our approach can be seen, in s...

2006
YUANJI CHENG

In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent −∆u = λu− αu + u −1, u > 0, in Ω, u = 0, on ∂Ω. where Ω ⊂ Rn, n ≥ 3 is a bounded C2-domain λ > λ1, 1 < p < 2∗ − 1 = n+2 n−2 and α > 0 is a bifurcation parameter. Brezis and Nirenberg [2] showed that a lower order (non-negative) perturbation can contribute t...

2011
MARKUS KUNZE JAN VAN NEERVEN

We prove convergence of the solutions Xn of semilinear stochastic evolution equations on a Banach space B, driven by a cylindrical Brownian motion in a Hilbert space H, dXn(t) = (AnX(t) + Fn(t,Xn(t))) dt+Gn(t,Xn(t)) dWH(t), Xn(0) = ξn, assuming that the operators An converge to A and the locally Lipschitz functions Fn and Gn converge to the locally Lipschitz functions F and G in an appropriate ...

Journal: :Nonlinearity 2023

Abstract We consider the inverse problem of determining some class nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study stability issue for this problems. Under suitable assumptions, prove a Lipschitz and Hölder estimate associated with determination quasilinear semilinear equations measurements restricted to arbitrary part domain. Besides their...

Journal: :SIAM Journal on Optimization 2008
Eduardo Casas Juan Carlos de los Reyes Fredi Tröltzsch

Abstract. Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associat...

Journal: :SIAM Journal of Applied Mathematics 2018
Kui Ren Rongting Zhang

Two-photon photoacoustic tomography (TP-PAT) is a non-invasive optical molecular imaging modality that aims at inferring two-photon absorption property of heterogeneous media from photoacoustic measurements. In this work, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients in a semilinear elliptic PDE, the mathematical model for the propagati...

2005
Jean Dolbeault Javier Fernández Óscar Sánchez

We consider the two dimensional gravitational VlasovPoisson system. Using variational methods, we prove the existence of stationary solutions of minimal energy under a Casimir type constraint. The method also provides a stability criterion of these solutions for the evolution problem. Key-words. Vlasov-Poisson system – stellar dynamics – polytropic gas spheres – gravitation – mass – energy – ki...

2011
Yūki Naito Tokushi Sato

where λ > 0 is a parameter, κ ∈ R is a constant, p = (N + 2)/(N − 2) is the critical Sobolev exponent, and f(x) is a non-homogeneous perturbation satisfying f ∈ H−1(Ω) and f ≥ 0, f ≡ 0 in Ω. Let κ1 be the first eigenvalue of −Δ with zero Dirichlet condition on Ω. Since (1.1)λ has no positive solution if κ ≤ −κ1 (see Remark 1 below), we will consider the case κ > −κ1. Let us recall the results f...

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