Results 81 to 90 of about 1,398 (233)
Super and subsolutions for elliptic equations on all of ℝn
International Journal of Mathematics and Mathematical Sciences, 2002 By construction sub and supersolutions for the following semilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn which arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the
G. A. Afrouzi, H. Ghasemzadeh
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Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers
, 2001 In this paper we construct new classes of stationary solutions for the Cahn-Hilliard equation by a novel approach. One of the results is as follows: Given a positive integer K and a (not necessarily nondegenerate) local minimum point of the mean
Winter, M, Wei, J
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Existence results for a class of semilinear degenerate elliptic equations [PDF]
, 2003 summary:We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form.
Bonafede, Salvatore
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Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
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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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Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball
, 2004 In [40], it was shown that the following singularly perturbed Dirichlet problem \ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\] \[ u=0 \ \mbox{on} \ \partial \Om has a nodal solution u_\ep which has the least energy among all nodal solutions.
Winter, M +5 more
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A nonlinear characterization of stochastic completeness of graphs
Mathematische Nachrichten, Volume 298, Issue 3, Page 925-943, March 2025.Abstract We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem.
Marcel Schmidt, Ian Zimmermann
wiley +1 more source
Solutions to nonlinear elliptic equations with a nonlocal boundary condition
Electronic Journal of Differential Equations, 2002 We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated.
Yuandi Wang
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Abstract and Applied Analysis, 2010 We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation −Δ𝑢+𝑢=𝜆𝑎(𝑥)|𝑢|𝑞−2𝑢+𝑏(𝑥)|𝑢|𝑝−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), where 𝜆>0 ...
Tsing-San Hsu, Huei-Li Lin
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Local versus nonlocal elliptic equations: short-long range field interactions
Advances in Nonlinear Analysis, 2020 In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian.
Cassani Daniele +2 more
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