scholarly journals Existence of strong solutions of ap(x)-Laplacian Dirichlet problem without the Ambrosetti–Rabinowitz condition

2015 ◽  
Vol 69 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Qihu Zhang ◽  
Chunshan Zhao
2012 ◽  
Vol 64 (1) ◽  
pp. 217-240 ◽  
Author(s):  
Lin Tang

AbstractIn this paper, we establish the regularity of strong solutions to nondivergence parabolic equations with BMO coefficients in nondoubling weighted spaces.


1996 ◽  
Vol 39 (1) ◽  
pp. 31-36
Author(s):  
Gabriele Bonanno

In this note we consider the Dirichlet problem Δu + f(x, u)=0 in Ω, u = 0 on ∂Ω here Ω is a bounded domain in ℝn(n≧3), with smooth boundary ∂Ω. We prove the existence of strong solutions to the previous problem, which are positive if f satisfies a suitable condition. As a consequence we find that the problem with , may have positive solutions even if g is not a lower-order perturbation of Next We examine the case .


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