Results 81 to 90 of about 75,181 (273)
Radial solutions to semilinear elliptic equations via linearized operators
Electronic Journal of Qualitative Theory of Differential Equations, 2017 Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative.
Phuong Le
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Semilinear elliptic equations on unbounded domains
Mathematische Zeitschrift, 1985 A variational proof is given for the existence of a nontrivial non- negative weak solution, having certain symmetric properties, for a non- autonomous boundary value problem \(-\Delta u-\lambda u=r(x)f(u(x)),\quad x\in \Omega,\quad u\in H^ 1_ 0(\Omega).\) Here f is a given increasing continuous function satisfying certain superlinear growth conditions,
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Holomorphic extension of solutions of semilinear elliptic equations [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2011 We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of $\mathbb{C}^d$, improving earlier results where the extension was shown for a strip.
CAPPIELLO, Marco, F. Nicola
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A posteriori error estimation and adaptivity for temporal multiscale problems
PAMM, Volume 24, Issue 4, December 2024.Abstract In science and engineering, problems over multiple scales in time often arise. Two examples are material damage in oscillating structures or plaque growth in pulsating blood vessels. Here the long term effects are of interest but they depend on the coupled fast‐changing physical processes which must be taken into account.
Leopold Lautsch, Thomas Richter
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Uniqueness of positive solutions for cooperative Hamiltonian elliptic systems
Electronic Journal of Differential Equations, 2016 The uniqueness of positive solution of a semilinear cooperative Hamiltonian elliptic system with two equations is proved for the case of sublinear and superlinear nonlinearities. Implicit function theorem, bifurcation theory, and ordinary differential
Junping Shi, Ratnasingham Shivaji
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Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type [PDF]
Opuscula Mathematica, 2006 A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered.
Tomasz S. Zabawa
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Bifurcation for indefinite‐weighted p$p$‐Laplacian problems with slightly subcritical nonlinearity
Mathematische Nachrichten, Volume 297, Issue 11, Page 3982-4002, November 2024.Abstract We study a superlinear elliptic boundary value problem involving the p$p$‐Laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the corresponding linear weighted boundary value problem.
Mabel Cuesta, Rosa Pardo
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On the maximum field of linearity of linear sets
Bulletin of the London Mathematical Society, Volume 56, Issue 11, Page 3300-3315, November 2024.Abstract Let V$V$ denote an r$r$‐dimensional Fqn$\mathbb {F}_{q^n}$‐vector space. For an m$m$‐dimensional Fq$\mathbb {F}_q$‐subspace U$U$ of V$V$, assume that dimq⟨v⟩Fqn∩U⩾2$\dim _q \left(\langle {\bf v}\rangle _{\mathbb {F}_{q^n}} \cap U\right) \geqslant 2$ for each nonzero vector v∈U${\bf v}\in U$. If n⩽q$n\leqslant q$, then we prove the existence of
Bence Csajbók +2 more
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Leapfrogging vortex rings for the three‐dimensional incompressible Euler equations
Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 3843-3957, October 2024.Abstract A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three‐dimensional fluid. In 1858, Helmholtz observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on ...
Juan Dávila +3 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
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