2014/09/20 by Biagio Ricceri, Ricceri, Biagio
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1409.5919
openalex publication_date 2014/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, using the theory developed in [8], we obtain some results of a\ntotally new type about a class of non-local problems. Here is a sample:\n Let \Ω\⊂ bf Rn be a smooth bounded domain, with n\≥ 4, let\na, b, \ν\∈ bf R, with a\≥ 0 and b>0, and let p\∈ ]\n0,n+2 over n-2 [.\n Then, for each \λ>0 large enough and for each convex set C\⊆\nL2(\Ω) whose closure in L2(\Ω) contains H10(\Ω), there\nexists v^*\∈ C such that the problem
cases -
left (\na+b
int
Omega|
nabla u(x)|2dx
right )
Delta u\n=
nu|u|p-1u+
lambda(u-v^*(x)) amp; in
Omega
cr amp;
cr u=0 amp; on\n
partial
Omega
cr has at least three weak solutions, two of which are\nglobal minima in H10(\Ω) of the corresponding energy functional.\n