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Critical points of the regular part of the harmonic Green function with Robin boundary condition
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2008-09-01)
In this paper we consider the Green function for the Laplacian in a smooth bounded domain Omega subset of R-N with Robin boundary condition
partial derivative G(lambda)/partial derivative nu + lambda b(x)G(lambda) = 0, ...
Singular limits for the bi-Laplacian operator with exponential nonlinearity in R-4
(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2008-10)
Let Omega be a bounded smooth domain in R-4 such that for some integer d >= 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem
{Delta(2)u - rho(4)k(x)e(u) = 0 in Omega,
u = ...
Bubble tower solutions for a supercritical elliptic problem in R-N
(SCUOLA NORMALE SUPERIORE, 2016)
We consider the problem {-Delta u + u = u(p) + lambda u(q) u > 0 in R-Nu(z) -> 0 as vertical bar z vertical bar -> infinity where p = p* + epsilon, with p* = N+2/N-2, while 1 < q < N+2/N-2 if N >= 4, and 3 < q < 5 if N = ...
"Bubble-Tower" phenomena in a semilinear elliptic equation with mixed Sobolev growth
(PERGAMON-ELSEVIER SCIENCE LTD, 2008-03-01)
In this work we consider the following problem
[GRAPHICS]
with N/(N - 2) < p < p* = (N + 2)/(N - 2) < q, N >= 3.
We prove that if p is fixed, and q is close enough to the critical exponent p*, then there exists a ...
New type of solutions to a slightly subcritical Henon type problem on general domains
(Elsevier, 2017)
We consider the following slightly subcritical problem
((sic)epsilon) { -Delta u = beta(x)vertical bar u vertical bar(p-1-epsilon) u in Omega, u = 0 on partial derivative Omega,
where Omega is a smooth bounded ...
Green's function and infinite-time bubbling in the critical nonlinear heat equation
(European Mathematical Society, 2020)
Let Omega be a smooth bounded domain in R-n, n >= 5. We consider the classical semilinear heat equation at the critical Sobolev exponent.
ut =Delta u + un+2/n-2 in Omega x (0, infinity), u = 0 on partial derivative Omega ...