منابع مشابه
p-Laplacian problems with critical Sobolev exponent
We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.
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Article history: Received 8 April 2015 Available online 12 August 2015 Submitted by R.G. Durán
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In this article, we study eigenvalue problems with the p-Laplacian operator: −(|y′|p−2y′)′ = (p− 1)(λρ(x)− q(x))|y|p−2y on (0, πp), where p > 1 and πp ≡ 2π/(p sin(π/p)). We show that if ρ ≡ 1 and q is singlewell with transition point a = πp/2, then the second Neumann eigenvalue is greater than or equal to the first Dirichlet eigenvalue; the equality holds if and only if q is constant. The same ...
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Under suitable assumptions on the potential of the nonlinearity, we study the existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplacian. Our approach is based on variational methods.
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We consider a number of boundary value problems involving the p-Laplacian. The model case is −∆pu = V |u|p−2u for u ∈ W 1,p 0 (D) with D a bounded domain in R. We derive necessary conditions for the existence of nontrivial solutions. These conditions usually involve a lower bound for a product of powers of the norm of V , the measure of D, and a sharp Sobolev constant. In most cases, these ineq...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2018
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-018-1416-9