منابع مشابه
Some Integral Equations with Nonsymmetric Separable Kernels*
Absbact. It is shown that the eigeovalues and eigenfunctions for the class of "separable" or "semidegenerate" kernels can be determined from the solution of a linear differential equation, which is usually more amenable to machine solution. The theory is extended to solve a simultaneous diagonalization problem for two separable kernels. Finally, some new connections are obtained between Riccati...
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Abstract. Many applications give rise to separable parameterized equations, which have the form A(y, μ)z + b(y, μ) = 0, where z ∈ R , y ∈ R, μ ∈ R, and the (N + n)×N matrix A(y, μ) and (N + n) vector b(y, μ) are C-Lipschitzian in (y, μ) ∈ Ω ⊂ R × R. We present a technique which reduces the original equation to the form f(y, μ) = 0, where f : Ω → R is C-Lipschitzian in (y, μ). This reduces the d...
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For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( x |x|). The problem reduces to a quasilinear elliptic equation on S and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral ty...
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W. MILLER †, E. KALNINS ‡ and G. POGOSYAN § † School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455, U.S.A. E-mail: [email protected] ‡ Department of Mathematics, University of Waikato, Hamilton, New Zealand E-mail: [email protected] § Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 14980 Dubna, Moscow Region, Russia E-mail: pogosyan@thsun...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2002
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1436563