Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities

Li, Anran; Cai, Hongrui; Su, Jiabao

doi:10.12775/tmna.2014.026

Cited by 7 publications

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References 13 publications

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“…Since V satisfies (20) with γ 0 = −a (cf. Remark 2.8.4 for the best choice of γ 0 ), we apply Theorem 2.1 together with Theorems 2.3 and 2.7, where assumptions (10) and (19)…”

Section: Example 35 Consider the Potentialmentioning

confidence: 99%

Compactness and existence results for the p-Laplace equation

Badiale¹,

Guida²,

Rolando³

2017

Journal of Mathematical Analysis and Applications

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Given 1 < p < N and two measurable functions V (r) ≥ 0 and K (r) > 0, r > 0, we define the weighted spacesand study the compact embeddings of the radial subspace ofas a particular case. We consider exponents q1, q2, q that can be greater or smaller than p. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately. We then apply these results to the investigation of existence and multiplicity of finite energy solutions to nonlinear p-Laplace equations of the formwhere V and g (|·| , u) with u fixed may be vanishing or unbounded at zero or at infinity. Both the cases of g super and sub p-linear in u are studied and, in the sub p-linear case, nonlinearities with g (|·| , 0) = 0 are also considered. MSC (2010):Primary 35J92; Secondary 35J20, 46E35, 46E30

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“…Since V satisfies (20) with γ 0 = −a (cf. Remark 2.8.4 for the best choice of γ 0 ), we apply Theorem 2.1 together with Theorems 2.3 and 2.7, where assumptions (10) and (19)…”

Section: Example 35 Consider the Potentialmentioning

confidence: 99%