Displaying similar documents to “Boundary value problems for nonlinear perturbations of some ϕ-Laplacians”

Nonlinear systems with mean curvature-like operators

Pierluigi Benevieri, João Marcos do Ó, Everaldo Souto de Medeiros (2007)

Banach Center Publications

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We give an existence result for a periodic boundary value problem involving mean curvature-like operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.

Bound sets and two-point boundary value problems for second order differential systems

Jean Mawhin, Katarzyna Szymańska-Dębowska (2019)

Mathematica Bohemica

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The solvability of second order differential systems with the classical separated or periodic boundary conditions is considered. The proofs use special classes of curvature bound sets or bound sets together with the simplest version of the Leray-Schauder continuation theorem. The special cases where the bound set is a ball, a parallelotope or a bounded convex set are considered.

On unbounded solutions for differential equations with mean curvature operator

Zuzana Došlá, Mauro Marini, Serena Matucci (2025)

Czechoslovak Mathematical Journal

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We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived.

Boundaries of prescribed mean curvature

Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The existence of a singular curve in R 2 is proven, whose curvature can be extended to an L 2 function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.