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1.
Mabel Cuesta Humberto Ramos Quoirin 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(4):469-491
Let Δ
p
denote the p-Laplacian operator and Ω be a bounded domain in . We consider the eigenvalue problem
for a potential V and a weight function m that may change sign and be unbounded. Therefore the functional to be minimized is indefinite and may be unbounded from below.
The main feature here is the introduction of a value α(V, m) that guarantees the boundedness of the energy over the weighted sphere . We show that the above equation has a principal eigenvalue if and only if either m ≥ 0 and α(V, m) > 0 or m changes sign and α(V, m) ≥ 0. The existence of further eigenvalues is also treated here, mainly a second eigenvalue (to the right) and their dependence
with respect to V and m.
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2.
J. Tervo 《Aequationes Mathematicae》1990,40(1):201-234
The paper deals with the minimal and the maximal realizations (L
w
)~ and (L
w
):L
2L
2 of linear operators of Weyl type
} dy} } \right)d\xi }$$
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3.
Maria Lianantonakis 《Journal of Geometric Analysis》2000,10(2):299-322
A weighted Laplace-Beltrami operator on a Riemannian manifold M is an operator of the form
4.
In this paper, we consider a nonlinear elliptic equation driven by the p-Laplacian and with a parameter λ > 0. Using a combination of variational and degree theoretic methods, we show that there
exists λ* > 0 such that, if λ > λ*, then the problem has two positive smooth solutions. Our result extends earlier ones by Rabinowitz (semilinear equations)
and Guo (nonlinear equations).
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5.
A. M. El-Sayed 《Periodica Mathematica Hungarica》1988,19(2):143-147
In the present work it is studied the initial value problem for an equation in the form
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