Positive solutions of some nonlinear elliptic problems in exterior domains

Benci, Vieri; Cerami, Giovanna

doi:10.1007/bf00282048

Cited by 263 publications

(251 citation statements)

References 13 publications

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“…Beside the case when p → 2 * , the papers [1,2] treat also when a certain parameter λ appearing in the equation tends to +∞. We do not enter in details here, but the same type of result is obtained: for large λ the domain topology gives a lower bound on the number of positive solutions of the problem.…”

Section: Introductionmentioning

confidence: 89%

“…In case of a non contractible domain Ω, the existence of another solution can be obtained with the same arguments of [2] (see also [8]). This is classical by now, but for completeness we recall the proof.…”

mentioning

confidence: 92%

“…In the celebrated papers [1,2] Benci, Cerami and Passaseo proved an existence result of positive solutions of the following problem (1.1)…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, after the papers [1][2][3], many authors have used the same methods to prove multiplicity results of solutions (depending on the domain topology) whenever λ → +∞, that is for problems in expanding domains, or ε → 0, that is for semiclassical states.…”

Section: Introductionmentioning

confidence: 99%

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Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

Figueiredo

Siciliano

2017

Nonlinear Analysis: Real World Applications

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Section: Introductionmentioning

confidence: 89%

mentioning

confidence: 92%

“…In the celebrated papers [1,2] Benci, Cerami and Passaseo proved an existence result of positive solutions of the following problem (1.1)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

Figueiredo

Siciliano

2017

Nonlinear Analysis: Real World Applications

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“…Proof. We use the characterization of the Palais-Smale sequences as given in [4], see also [39], by also taking the symmetry into account. Namely, since c < 2 c 0 (R N ) we have that, for some k points…”

Section: Lemma 414 We Have Thatmentioning

confidence: 99%

Ground state and non-ground state solutions of some strongly coupled elliptic systems

Bonheure

Santos²,

Ramos

2011

Trans. Amer. Math. Soc.

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Abstract. We study an elliptic system of the form Lu = |v| p−1 v and Lv = |u| q−1 u in Ω with homogeneous Dirichlet boundary condition, where Lu := −Δu in the case of a bounded domain and Lu := −Δu + u in the cases of an exterior domain or the whole space R N . We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

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Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients

Cerami

Passaseo

Solimini

2012

Comm Pure Appl Math

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In this paper the equation $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}} - \Delta u + a(x)u = |u|^{p - 1} u\;{\rm in }\;{\R}^N $ is considered, when N ≥ 2, p > 1, and $p < {{N + 2} \over {N - 2}}$ if N ≥ 3. Assuming that the potential a(x) is a positive function belonging to $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}L_{{\rm loc}}^{N/2} ({\R}^N )$ such that a(x) → a∞ > 0 as |x|→∞ and satisfies slow decay assumptions but does not need to fulfill any symmetry property, the existence of infinitely many positive solutions, by purely variational methods, is proved. The shape of the solutions is described as is, and furthermore, their asymptotic behavior when $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}|a(x) - a_\infty |_{L_{{\rm loc}}^{N/2} ({\R}^N )} \to 0$. © 2012 Wiley Periodicals, Inc.

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Positive solutions of some nonlinear elliptic problems in exterior domains

Cited by 263 publications

References 13 publications

Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

Ground state and non-ground state solutions of some strongly coupled elliptic systems

Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients

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