Search results for "Palais-Smale condition"

showing 3 items of 3 documents

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Class (set theory)geographyPure mathematicsgeography.geographical_feature_categorycritical pointsGeneral Mathematicsthree solutions58E30two-point boundary value problemPalais-Smale conditionmountain pass34B1558E05A mountain pass theoremCombinatoricsPalais–Smale compactness conditionSettore MAT/05 - Analisi MatematicaMountain pass theoremMountain pass49J4047J30Mathematics
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The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

2022

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the spac…

General Mathematicsregularized problem(<i>r</i>(<i>u</i>)<i>s</i>(u))-Laplacian operatorPalais-Smale conditionweak solutionComputer Science::Digital Libraries(<i>r</i>(<i>u</i>)<i>s</i>(u))-Laplacian operator; Palais-Smale condition; monotone operator; regularized problem; weak solutionSettore MAT/05 - Analisi Matematicamonotone operatorComputer Science (miscellaneous)QA1-939Computer Science::Programming Languages(r(u) s(u))-Laplacian operatorEngineering (miscellaneous)MathematicsMathematics
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A min-max principle for non-differentiable functions with a weak compactness condition

2009

A general critical point result established by Ghoussoub is extended to the case of locally Lipschitz continuous functions satisfying a weak Palais-Smale hypothesis, which includes the so-called non-smooth Cerami condition. Some special cases are then pointed out.

Pure mathematicsApplied MathematicsMathematics::Analysis of PDEsGeneral MedicineLipschitz continuityCritical point (mathematics)Critical pointLocally lipshitz continuous functionCompact spaceWeak Palais-Smale conditionDifferentiable functionMountain Pass geometryAnalysisMathematicsCommunications on Pure &amp; Applied Analysis
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