Results 21 to 30 of about 470 (37)
Conformally covariant parameterizations for relativistic initial data
, 2016 We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems.
Delay, Erwann
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Elliptic equations involving general subcritical source nonlinearity and measures [PDF]
, 2014 In this article, we study the existence of positive solutions to elliptic equation (E1) $$(-\Delta)^\alpha u=g(u)+\sigma\nu \quad{\rm in}\quad \Omega,$$ subject to the condition (E2) $$u=\varrho\mu\quad {\rm on}\quad \partial\Omega\ \ {\rm if}\ \alpha=1 ...
Chen, Huyuan +2 more
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Semilinear fractional elliptic equations with gradient nonlinearity involving measures [PDF]
, 2013 We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where $\epsilon=1$ or
Chen, Huyuan, Veron, Laurent
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Boundary regularity, Pohozaev identities, and nonexistence results
, 2017 In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $\Omega$, $u\equiv0$ in $\mathbb R^n\backslash\Omega$. We first discuss in detail the boundary regularity of solutions, stating the main known results
Ros-Oton, Xavier
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Semilinear fractional elliptic equations involving measures [PDF]
, 2013 We study the existence of weak solutions of (E) $ (-\Delta)^\alpha u+g(u)=\nu $ in a bounded regular domain $\Omega$ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus\Omega$, where $(-\Delta)^\alpha$ denotes the fractional Laplacian with $\alpha\in(0,1)$,
Chen, Huyuan, Veron, Laurent
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An indefinite concave-convex equation under a Neumann boundary condition II
, 2016 We proceed with the investigation of the problem $(P_\lambda): $ $-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \ \mbox{ in } \Omega, \ \ \frac{\partial u}{\partial \mathbf{n}} = 0 \ \mbox{ on } \partial \Omega$, where $\Omega$ is a bounded smooth ...
Quoirin, Humberto Ramos +1 more
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Nonlinear elliptic equations and systems with linear part at resonance
, 2016 The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues.
Korman, Philip
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Monotonicity and Symmetry of Nonnegative Solutions to -Δ u=f(u) in Half-Planes and Strips. [PDF]
Adv Nonlinear Stud, 2017 Farina A, Sciunzi B.
europepmc +1 more source