Solutions for a Resonant Elliptic System With Coupling In

Furtado, Marcelo F.; Maia, Liliane A.; Silva, Elves A. B.

doi:10.1081/pde-120005847

Cited by 33 publications

(21 citation statements)

References 23 publications

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“…It is a metric space, and W (u) ∩B is an open set in this space. Thus, {W (u) ∩B} for u ∈B is an open covering of the paracompact spaceB (see for example [Kelley 1955]). Consequently, there is a locally finite refinement {W τ } of this cover.…”

Section: Weak Sandwich Pairsmentioning

confidence: 99%

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Infinite-dimensional sandwich pairs

Schechter¹

2008

Pacific J. Math.

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For many equations arising in the physical sciences, the solutions are critical points of functionals. This has led to interest in finding critical points of such functionals. If a functional G is semibounded, one can find PalaisSmale (PS) sequences G(u k ) → a and G (u k ) → 0. These sequences produce critical points if they have convergent subsequences (that is, if G satisfies the PS condition). However, there is no clear method of finding critical points of functionals that are not semibounded. In this paper we find pairs of sets having the property that functionals bounded from below on one set and bounded from above on the other have PS sequences. We can allow both sets to be infinite-dimensional if we make a slight additional smoothness requirement on the functional. This allows us to solve systems of equations that could not be solved before.

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Section: Weak Sandwich Pairsmentioning

confidence: 99%

“…Such systems have been studied in the literature by many authors (for example, Costa and Magalhães 1994;de Figueiredo and Felmer 1994;Furtado and Silva 2001;Furtado et al 2002a;2002b;Li and Yang 2004;Schechter 1998 and the literature quoted in them). Let λ 0 (µ 0 ) be the lowest eigenvalue of ‫.…”

Section: Applicationsmentioning

confidence: 99%

Infinite-dimensional sandwich pairs

Schechter¹

2008

Pacific J. Math.

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“…> 0 and any fixed λ > 0) when f : R → R is subcritical, odd and verifies (AR). Furtado, Maia and Silva [7] studied (P λ ) in the case when F : R → R (defined in (AR)) has some sort of resonance with a local nonquadraticity condition at infinity, while the potential a verifies (BW ). Gazzola and Rȃdulescu [8] studied (P λ ) when a verifies (BW ), f is not necessarily continuous and satisfies an appropriate non-smooth (AR) condition.…”

Section: Alexandru Kristály Nodeamentioning

confidence: 99%

“…In particular, studying closely related problems to (P λ ), many authors use the Ambrosetti-Rabinowitz type condition (see [2], [4], [5]) or some of its variant (see [1], [8], [7]):…”

Section: Alexandru Kristály Nodeamentioning

confidence: 99%

Multiple solutions of a sublinear Schrödinger equation

Kristály

2007

Nonlinear differ. equ. appl.

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Abstract. In this paper we study the Schrödinger equation of the formwhere λ > 0 is a parameter, a and b are positive potentials, while the nonlinear term f : R → R is sublinear at infinity. Two cases will be considered:(i) f is superlinear at the origin; (ii) f does not satisfy any asymptotical property at the origin. In both situations, the existence of certain multiple weak solutions of (P λ ) are established for some λ > 0.2000 Mathematics Subject Classification: 35J60, 35J65.

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“…The functional is unbounded from above and below on infinite dimensional subspaces. This situation has been attacked before under quite strong hypotheses (cf., e.g., [1][2][3][4][5][6][7]11,13,[19][20][21]24,25,28,30,31] and the references contained there). The purpose of the present paper is to weaken the hypotheses considerably.…”

Section: Introductionmentioning

confidence: 99%