An eigenvalue problem for generalized Laplacian in Orlicz—Sobolev spaces

DOI10.1017/S0308210500027505zbMath0926.46030MaRDI QIDQ4243034

Matti Tienari, Vesa Mustonen

Publication date: 22 November 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

weak solutionminimization problem\(\Delta_2\)-conditionEuler-Lagrange equation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) General theory of partial differential operators (47F05)

Related Items (22)

Fractional eigenvalues in Orlicz spaces with no \(\Delta_2\) condition ⋮ Nonlinear eigenvalues for a quasilinear elliptic system in Orlicz-Sobolev spaces ⋮ Minimization problems for inhomogeneous Rayleigh quotients ⋮ The limiting Behavior of Solutions to Inhomogeneous Eigenvalue Problems in Orlicz-Sobolev Spaces ⋮ Some existence results and properties of solutions in quasilinear variational inequalities with general growths ⋮ An eigenvalue problem for the anisotropic \(\Phi \)-Laplacian ⋮ Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces ⋮ Variational eigenvalues of the fractional g-Laplacian ⋮ The eigenvalue problem for quasilinear elliptic operators with general growth ⋮ A Lions type result for a large class of Orlicz-Sobolev space and applications ⋮ Optimal design problems for a degenerate operator in Orlicz-Sobolev spaces ⋮ Orlicz-Sobolev algebras ⋮ Asymptotic properties of a $\varphi$-Laplacian and Rayleigh quotient ⋮ Ljusternik-Schnirelmann theorem for the generalized Laplacian ⋮ A direct approach to Orlicz-Sobolev capacity ⋮ AN EIGENVALUE PROBLEM FOR A CLASS OF NONLINEAR ELLIPTIC OPERATORS ⋮ On a nonlinear eigenvalue problem for generalized Laplacian in Orlicz-Sobolev spaces ⋮ Lagrange Multiplier Rule to a Nonlinear Eigenvalue Problem in Musielak–Orlicz Spaces ⋮ Eigenvalue problem associated with nonhomogeneous integro-differential operators ⋮ Eigenvalues and minimizers for a non-standard growth non-local operator ⋮ Generic existence result for an eigenvalue problem with rapidly growing principal operator ⋮ Existence of solution for a class of quasilinear elliptic problem without Δ2-condition

Cites Work

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• Spectral analysis of nonlinear operators
• Orlicz-Sobolev spaces and imbedding theorems
• Variational inequalities in Orlicz-Sobolev spaces
• Positive solutions for the p-Laplacian: application of the fibrering method

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