On the asymptotics of solutions of the Lane-Emden problem for the \(p\)-Laplacian

DOI10.1007/s00013-008-2854-yzbMath1154.35067OpenAlexW1978727719MaRDI QIDQ998958

Christopher Grumiau, Enea Parini

Publication date: 30 January 2009

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-008-2854-y

zbMATH Keywords

energy functional\(p\)-Laplacianground state solutionsleast energy nodal solutions(nodal) Nehari manifoldfirst and second eigenfunctions of - \(\Delta _{p }\)

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20)

Related Items (11)

On the asymptotic behavior of certain solutions of the Dirichlet problem for the equation \({-\Delta_pu=\lambda| u|^{q-2}u}\) ⋮ Limits as \(p \rightarrow \infty \) of \(p\)-Laplacian eigenvalue problems perturbed with a concave or convex term ⋮ Towards existence theorems to affine \(p\)-Laplace equations via variational approach ⋮ Least energy solutions to the Dirichlet problem for the equation −Δu=f(x,u) ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ A problem involving the p-Laplacian operator ⋮ Positivity for fourth-order semilinear problems related to the Kirchhoff-love functional ⋮ Remarks on the behavior of the best Sobolev constants ⋮ Limits as \(p\rightarrow\infty \) of \(p\)-Laplacian problems with a superdiffusive power-type nonlinearity: positive and sign-changing solutions ⋮ On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations ⋮ On the resonant Lane–Emden problem for the p-Laplacian

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