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Eigenvalue problems for quasilinear elliptic equations on \(R^ N\). (English) Zbl 0692.35045

We study the existence of standing waves of Schrödinger equations, the existence of nontrivial weak solutions of the eigenvalue problems of quasilinear elliptic scalar field equations and the decay at infinity of weak solutions of a class of quasilinear elliptic equations.

MSC:

35J60 Nonlinear elliptic equations
35J10 Schrödinger operator, Schrödinger equation
35P99 Spectral theory and eigenvalue problems for partial differential equations
35Q99 Partial differential equations of mathematical physics and other areas of application
35B40 Asymptotic behavior of solutions to PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:

[1] Lions P.L., Ann. Inst. Henri Poincare-Analyse non lineaire 1 pp 223– (1984)
[2] Xi-Ping Zhu, to appear in Acta Math. Sci..
[3] Lions P.L., Ann. Inst. Henri Poincare-Analyse non lineaire 1 pp 109– (1984)
[4] Brezis H., Commun. Math. Phys. 96 pp 97– (1984) · Zbl 0579.35025
[5] Li Gongbao, On the regularity of weak solutions of nonlinear scalarfield equation, to appear
[6] Tolksdorf Peter, J. Diff. Equ. 51 pp 126– (1984) · Zbl 0488.35017
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