Partial differential equations involving subcritical, critical and supercritical nonlinearities

Lorca, Sebastián; Ubilla, Pedro

doi:10.1016/j.na.2003.09.002

Cited by 12 publications

(27 citation statements)

References 14 publications

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“…Concerning with local assumptions, we mention that in [19], Nakao considered linear case with the condition 2a (t 2 )t + a(t) > 0 for any t ∈ R and, by using degree argument, they studied the existence of global branches from the least eigenvalue of −Δ and the trivial solution. Meanwhile, a more general setting was considered by Lorca and Ubilla in [16]. Under certain local hypotheses on a and f , both independent of the x-variable, and by imposing local monotonicity assumptions at zero, they showed the existence of solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence of solution for quasilinear equations involving local conditions

Cerda¹,

Iturriaga²

2019

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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In this paper, we study the existence of weak solutions of the quasilinear equation \begin{cases} -{\rm div} (a(\vert \nabla u \vert ^2)\nabla u)=\lambda f(x,u) &{\rm in} \ \Omega,\\ u=0 &{\rm on} \ \partial\Omega, \end{cases}where a : ℝ → [0, ∞) is C1 and a nonincreasing continuous function near the origin, the nonlinear term f : Ω × ℝ → ℝ is a Carathéodory function verifying certain superlinear conditions only at zero, and λ is a positive parameter. The existence of the solution relies on C1-estimates and variational arguments.

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Section: Introductionmentioning

confidence: 99%

Existence of solution for quasilinear equations involving local conditions

Cerda¹,

Iturriaga²

2019

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…In connection with multiplicity results for nonlinear problems with arbitrary perturbations, we mention the papers of Anello [1], Chen and Li [2], Iturriaga et al [3] and Lorca and Ubilla [5]. In [2,3,5] the authors deal with a nonlinear problem of the following type:…”

Section: Introductionmentioning

confidence: 99%

Bounded Multiple Solutions for -Laplacian Problems With Arbitrary Perturbations

Faraci¹,

Zhao

2015

J. Aust. Math. Soc.

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“…Among a few works for this problem, Lorca and Ubilla [14] studied this problem with a general nonlinearity including critical and supercritical cases, when the equation is nondegenerate, that is, the case when φ(0) > 0 and φ(t) is nonincreasing near t = 0. In this paper, motivated by [6,14], we consider the problem (1.1) with general φ(t), which includes Eq. (1.2) with critical nonlinearity, and give a nonnegative, nontrivial solution for appropriate functions a(x), b(x).…”

Section: Introductionmentioning

confidence: 99%