Large solutions for quasilinear elliptic equation with nonlinear gradient term

Chen, Yujuan; Wang, Mingxin

doi:10.1016/j.nonrwa.2010.06.031

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…Motivated by the results of the above cited papers, we shall attempt to treat such equation (1.1), the results of the semilinear equations are extended to the quasilinear ones. We can find the related results for m = 2 in [10].…”

Section: Introduction and Main Resultsmentioning

confidence: 65%

“…Then for some 0 < β < 1, there is a C 1,β -solution u of (2.2) such that u ≤ u ≤ū in Ω. The proof of the lemma 2.3 is similar to [10], so we omit it here. Definition 2.2.…”

Section: Proofs Of Theorem 11mentioning

confidence: 98%

“…Furthermore, if the blow-up lower solution and upper solution have the same blow-up rate near the boundary, we could get the asymptotic behavior of large solutions near the boundary. The idea of this section mainly comes from [10], [12]- [14].…”

Section: Proofs Of Theorem 11mentioning

confidence: 99%

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Existence of blow-up solutions for quasilinear elliptic equation with nonlinear gradient term

Yang

2014

Cubo

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In this paper, we consider the quasilinear elliptic equation in a smooth bounded domain. By using the method of lower and upper solutions, we study the existence, asymptotic behavior near the boundary and uniqueness of the positive blow-up solutions for quasilinear elliptic equation with nonlinear gradient term. RESUMEN En este artículo consideramos la ecuación elíptica cuasilineal en un dominio acotado suave. Usando el método de sub y súper soluciones, estudiamos la existencia, comportamiento asintótico cerca de la frontera y la unicidad de soluciones explosivas para ecuaciones elípticas cuasilineales con término del gradiente nolineal.

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Section: Introduction and Main Resultsmentioning

confidence: 65%

“…Then for some 0 < β < 1, there is a C 1,β -solution u of (2.2) such that u ≤ u ≤ū in Ω. The proof of the lemma 2.3 is similar to [10], so we omit it here. Definition 2.2.…”

Section: Proofs Of Theorem 11mentioning

confidence: 98%

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Existence of blow-up solutions for quasilinear elliptic equation with nonlinear gradient term

Yang

2014

Cubo

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“…Dirichlet and Neumann problems for a class of nonlinear degenerate elliptic equations with general growth in the gradient have been studied by Tian and Li in [10]. In the paper [5] by Chen and Wang the existence, asymptotic behavior near the boundary and uniqueness of large solutions for a class of quasilinear elliptic equations with a nonlinear gradient have been studied. Analogous problems to those treated in this paper have been considered among others by Abdellaoui in [1] and Hansson, Maz'ya and Verbitsky in [7].…”

Section: Introductionmentioning

confidence: 99%

Quasilinear elliptic equations with positive exponent on the gradient

Kraljević

Žubrinić

2013

Glas. Mat. Ser. III

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Abstract. We study the existence and nonexistence of positive, spherically symmetric solutions of a quasilinear elliptic equation (1.1) involving p-Laplace operator, with an arbitrary positive growth rate e 0 on the gradient on the right-hand side. We show that e 0 = p − 1 is the critical exponent: for e 0 < p−1 there exists a strong solution for any choice of the coefficients, which is a known result, while for e 0 > p − 1 we have existence-nonexistence splitting of the coefficientsf 0 andg 0 . The elliptic problem is studied by relating it to the corresponding singular ODE of the first order. We give sufficient conditions for a strong radial solution to be the weak solution. We also examined when ω-solutions of (1.1), defined in Definition 2.3, are weak solutions. We found conditions under which strong solutions are weak solutions in the critical case of e 0 = p − 1.

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