Nonexistence results and estimates for some nonlinear elliptic problems

Bidaut‐Véron, Marie‐Françoise; Pohožaev, Stanislav I.

doi:10.1007/bf02788105

Cited by 199 publications

(121 citation statements)

References 26 publications

Supporting

Mentioning

117

Contrasting

Unclassified

Order By: Relevance

“…Next we we prove local estimates of the second member F when F ∈ L 1 loc (Ω) and F ≧ 0,. following an idea of [10]:…”

Section: More Regularity Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On the Connection Between Two Quasilinear Elliptic Problems With Source Terms of Order 0 or 1

Hamid

Bidaut‐Véron

2010

Commun. Contemp. Math.

View full text Add to dashboard Cite

We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of R N . The first one, of the forminvolves a source gradient term with natural growth, where β is nonnegative, λ > 0, f (x) ≧ 0, and α is a nonnegative measure. The second one, of the formpresents a source term of order 0, where g is nondecreasing, and µ is a nonnegative measure. Here β and g can present an asymptote. The correlation gives new results of existence, nonexistence, regularity and multiplicity of the solutions for the two problems, without or with measures. New informations on the extremal solutions are given when g is superlinear.

show abstract

“…Next we we prove local estimates of the second member F when F ∈ L 1 loc (Ω) and F ≧ 0,. following an idea of [10]:…”

Section: More Regularity Resultsmentioning

confidence: 99%

“…Without assumption of convexity on g, we obtain local results, see Theorem 5.17, based on regularity results of [10] and Harnack inequality.…”

Section: Theorem 13mentioning

confidence: 99%

On the Connection Between Two Quasilinear Elliptic Problems With Source Terms of Order 0 or 1

Hamid

Bidaut‐Véron

2010

Commun. Contemp. Math.

View full text Add to dashboard Cite

show abstract

“…It is interesting that formally passing to the limit as k → ∞ in Theorem 1.2 we arrive at the sharp elliptic critical exponent q * ∞ = N +σ N −2 (see, for example, [22,23,24,13,16,5] and the references therein). Now let −∞ < σ ≤ −2.…”

Section: Resultsmentioning

confidence: 99%

Nonexistence results for higher–order evolution partial differential inequalities

Laptev

2002

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…The first one is a known local integral estimate (see [4,6,8]). Here and in the sequel, by B(x 0 ;R) we will mean a ball of radius R and center x 0 .…”

Section: Preliminariesmentioning

confidence: 99%

Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space

Lorca

2007

J. Inequal. Appl.

View full text Add to dashboard Cite

Nonexistence results and estimates for some nonlinear elliptic problems

Cited by 199 publications

References 26 publications

On the Connection Between Two Quasilinear Elliptic Problems With Source Terms of Order 0 or 1

On the Connection Between Two Quasilinear Elliptic Problems With Source Terms of Order 0 or 1

Nonexistence results for higher–order evolution partial differential inequalities

Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space

Contact Info

Product

Resources

About