Search results for " Nonlinear maximum principle"

showing 2 items of 2 documents

Positive solutions for the Neumann p-Laplacian

2017

We examine parametric nonlinear Neumann problems driven by the p-Laplacian with asymptotically ( $$p-1$$ )-linear reaction term f(z, x) (as $$x\rightarrow +\infty $$ ). We determine the existence, nonexistence and minimality of positive solutions as the parameter $$\lambda >0$$ varies.

Pure mathematicsPositive solutions Nonlinear regularity Nonlinear maximum principle Nonlinear Picone’s identityGeneral Mathematics010102 general mathematicsMathematical analysisLambda01 natural sciencesTerm (time)010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi Matematicap-Laplacian0101 mathematicsParametric statisticsMathematics
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Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems

2017

We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…

Sublinear functionMonotonic functionLambda01 natural sciencesOmegaDirichlet distributionsymbols.namesakeFirst eigenvalueP-LaplacianUniqueness0101 mathematicsEigenvalues and eigenvectorsMathematical physicsNonlinear regularityPhysicsApplied Mathematics010102 general mathematicsMathematical analysisVariational methodAnalysiFirst eigenvalue; Generalized picone's identity; Nonlinear maximum principle; Nonlinear regularity; P-Laplacian; Variational methods; Analysis; Applied MathematicsGeneral Medicine010101 applied mathematicsp-LaplaciansymbolsNonlinear maximum principleGeneralized picone's identityAnalysis
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