A limit involving functions in
Biagio Ricceri (1999)
Colloquium Mathematicae
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We point out the following fact: if Ω ⊂ is a bounded open set, δ>0, and p>1, then , where
Biagio Ricceri (1999)
Colloquium Mathematicae
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We point out the following fact: if Ω ⊂ is a bounded open set, δ>0, and p>1, then , where
Monica Musso, Angela Pistoia (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider the problem where and are smooth bounded domains in , , and We prove that if the size of the hole goes to zero and if, simultaneously, the parameter goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.
Sergio Campanato (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be a bounded open convex set of class . Let be a non linear operator satisfying the condition (A) (elliptic) with constants , , . We prove that a number is an eigenvalue for the operator if and only if the number is an eigen-value for the operator . If , the two systems and have the same solutions. In particular, also the eventual eigen-values of the operator should all be negative. Finally, we obtain a sufficient condition for the existence of solutions ...
Hongya Gao, Shuang Liang, Yi Cui (2016)
Czechoslovak Mathematical Journal
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The paper deals with very weak solutions , , to boundary value problems of the -harmonic equation We show that, under the assumption , , any very weak solution to the boundary value problem () is integrable with provided that is sufficiently close to .
P. Courilleau, S. Fabre, J. Mossino (2001)
Bollettino dell'Unione Matematica Italiana
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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo in un dominio limitato dello spazio -dimensionale; e sono matrici con coefficenti limitati, e è invertibile e la sua matrice inversa ha anche coefficenti limitati. La non linearità è dovuta alla funzione ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul -Laplaciano, , ed assicurano l'esistenza di...
Jacques Giacomoni, Ian Schindler, Peter Takáč (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We investigate the following quasilinear and singular problem, where is an open bounded domain with smooth boundary, , , , and . As usual, if , is arbitrarily large if , and if . We employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in . While following an approach due to Ambrosetti-Brezis-Cerami, we need to prove two new results of separate interest: a strong comparison principle...
Sergio Campanato (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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is a bounded open set of , of class and . In the cylinder we consider non variational basic operator where is a vector in , , which is continuous in and satisfies the condition (A). It is shown that the Cauchy-Dirichlet problem , in , has a unique solution. It is further shown that if is a solution of the basic system in , then and belong to . From this the Hölder continuity in of the vectors and are deduced respectively when and...