WITHDRAWN: New super-quadratic conditions for asymptotically periodic Schrödinger equation

Tang, Xianhua

doi:10.1016/j.jmaa.2014.12.044

Cited by 4 publications

(4 citation statements)

References 37 publications

(37 reference statements)

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“…The link theorems above mentioned have been used in a lot of papers, we would like to cite Chabrowski and Szulkin [5], doÓ and Ruf [8], Furtado and Marchi [9], Tang [30,31] and their references.…”

Section: Introductionmentioning

confidence: 99%

“…In [16], Li and Szulkin have improved this generalized link theorem to prove the existence of solution for a class of indefinite problem with f being asymptotically linear at infinity. The link theorems above mentioned have been used in a lot of papers, we would like to cite Chabrowski and Szulkin [5], do Ó and Ruf [8], Furtado and Marchi [9], Tang [30,31] and their references.…”

Section: Introductionmentioning

confidence: 99%

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Ground state solution for a class of indefinite variational problems with critical growth

Alves

Germano

2018

Journal of Differential Equations

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In this paper we study the existence of ground state solution for an indefinite variational problem of the typewhere N ≥ 2, V, W : R N → R and f : R N × R → R are continuous functions verifying some technical conditions and f possesses a critical growth. Here, we will consider the case where the problem is asymptotically periodic, that is, V is Z N -periodic, W goes to 0 at infinity and f is asymptotically periodic. (2010) Mathematics Subject ClassificationsThe reader is invited to see that if J is definite strongly, that is, when E − = {0}, the set O is exactly the Nehari manifold associated with J.Hereafter, we say thatIn [25], Szulkin and Weth have established the existence of ground state solution for problem (P 1 ) by completing the study made in [20], in the sense that, they also minimize the energy function on O, however they have used more weaker conditions on f , for example f is continuous, Z N -periodic in x and satisfies |f (x, t)| ≤ C(1 + |t| p−1 ), ∀t ∈ R and x ∈ R N (f 1 )

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ground state solution for a class of indefinite variational problems with critical growth

Alves

Germano

2018

Journal of Differential Equations

View full text Add to dashboard Cite

show abstract

“…The link theorems above mentioned have been used in a lot of papers, we would like to cite Chabrowski and Szulkin [5], do Ó and Ruf [7], Furtado and Marchi [9], Tang [25,26] and their references.…”

Section: Introductionmentioning

confidence: 99%

Existence of ground state solution and concentration of maxima for a class of indefinite variational problems

Alves¹,

Germano²

2020

Communications on Pure &Amp; Applied Analysis

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In this paper we study the existence of ground state solution and concentration of maxima for a class of strongly indefinite problem likeǫ where N ≥ 1, ǫ is a positive parameter, f : R → R is a continuous function with subcritical growth and V, A : R N → R are continuous functions verifying some technical conditions. Here V is a Z N -periodic function, 0 ∈ σ(−∆ + V ), the spectrum of −∆ + V , and 0 < inf x∈R N

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“…The link theorems above mentioned have been used in a lot of papers, we would like to cite Chabrowski and Szulkin [5], do Ó and Ruf [8], Furtado and Marchi [9], Tang [23,24] and their references.…”

Section: Introductionmentioning

confidence: 99%

Existence and Concentration Phenomena for a Class of Indefinite Variational Problems with Critical Growth

Alves

Germano

2018

Potential Anal

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In this paper we are interested to prove the existence and concentration of ground state solution for the following class of problemsf : R → R is a continuous function having critical growth, V : R N → R is a continuous and Z N -periodic function with 0 / ∈ σ(∆ + V ). By using variational methods, we prove the existence of solution for ǫ small enough. After that, we show that the maximum points of the solutions concentrate around of a maximum point of A. (2010): 35B40, 35J2, 47A10 . However, in [16], Pankov has found a ground state solution by minimizing the energy functional J on the set Mathematics Subject ClassificationsThe reader is invited to see that if J is strongly definite, that is, when E − = {0}, the set O is exactly the Nehari manifold associated with J. Hereafter, we say that u 0 ∈ H 1 (R N ) is a ground state solution if J ′ (u 0 ) = 0, u 0 ∈ O and J(u 0 ) = inf w∈O J(w).

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WITHDRAWN: New super-quadratic conditions for asymptotically periodic Schrödinger equation

Cited by 4 publications

References 37 publications

Ground state solution for a class of indefinite variational problems with critical growth

Ground state solution for a class of indefinite variational problems with critical growth

Existence of ground state solution and concentration of maxima for a class of indefinite variational problems

Existence and Concentration Phenomena for a Class of Indefinite Variational Problems with Critical Growth

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