On a Schrodinger equation with periodic potential and spectrum point zero

By Michel Willem, Wenming Zou. 2003

127 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/435785f7f1e74bfd22bb700a19a1474a52ac2c17

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. G. Lu
2. Xianhua Tang
3. Nguyen Huong Lam
4. Minbo Yang
5. Wenxiong CHEN *
6. Yanheng Ding
7. Nils Ackermann
8. Caifeng Zhang

In Computational Theory and Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Xianhua Tang
4. Minbo Yang
5. Nils Ackermann
6. Wenxiong CHEN *
7. Yanheng Ding
8. Caifeng Zhang

In Numerical Analysis

1. Minbo Yang
2. Nils Ackermann
3. Xianhua Tang
4. G. Lu
5. Wenxiong CHEN *
6. Nguyen Huong Lam
7. Yanheng Ding
8. Yong-Geun Oh

Citations in the corpus

• N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, unknown): “As far as the case when the nonlinear term f has the polynomial growth is concerned, we recall that, in [50], Willem and Zou used H(x, s) is increasing in s, ∀x ∈ Ω; s f (x, s) ≥ 0 ∀s ∈ R, s f (x, s) ≥ C0 |s|μ , ∀ |s| ≥ s0 > 0, ∀x ∈ Ω where μ > 2 and C0 > 0, instead of (AR).”
• Superlinear problems without Ambrosetti and Rabinowitz growth condition (2008, unknown): “On the other hand, Willem and Zou in [9] assumed H(x, s) ≡ sf (x, s) − 2F(x, s) is increasing in s, ∀x ∈ Ω, sf (x, s) 0, ∀s ∈ R, sf (x, s) C0|s|, |s| s0 > 0, ∀x ∈ Ω, where μ > 2 and C0 > 0, instead of condition (f ′).”
• Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms (2006, unknown): “, [1–3,5, 7,9–11, 13–18,22,23,25] and the references therein.”
• New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation (2014, unknown): “During the last several years, the existence of a nontrivial solution has been widely investigated in the literature, for example, see [2, 3, 7, 15, 19, 22] and references cited therein.”
• Solutions for Discrete Periodic Schrödinger Equations with Spectrum 0 (2010, methodology): “In [21, 24, 28 ], the authors developed monotonicity trick for strongly indefinite problem which is mainly due to Jeanjean [13] for studying Landesman-Lazer type problems in R N .”
• A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations (2006, background): “The two papers [9,46] treat the case where 0 is the left endpoint of a gap of the spectrum of T (see also [10]).”
• Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, methodology): “We recall that, in [44], Willem and Zou used H(x, s) is increasing in s, ∀x ∈ Ω; sf (x, s) ≥ 0.”
• The existence of a nontrivial solution to a nonlinear elliptic problem of linking type without the Ambrosetti-Rabinowitz condition (2011, unknown): “In [19], Willem and Zou studied (P ) for p = 2 and replaced the (AR) condition by the following conditions: H(x, s) , sf(x, s) − 2F (x, s) is nondecreasing in s for any x ∈ Ω, x ∈ R, sf(x, s) ≥ 0 for (x, s) ∈ Ω × R(1), and there exist constants s0 > 0, μ > 2, c0 > 0 such that sf(x, s) ≥ c0|s| for (x”
• New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, methodology): “1) in [3,32,33].”