Search results for " Nonlinear regularity"

showing 3 items of 3 documents

Positive solutions for singular (p, 2)-equations

2019

We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.

Dirichlet problemApplied MathematicsGeneral Mathematics010102 general mathematicsNonparametric statisticsSingular termGeneral Physics and AstronomyPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi MatematicaSingular term Superlinear perturbation Positive solution Nonlinear regularity Truncation Maximum principle Double phase problemApplied mathematics0101 mathematicsLaplace operatorMathematicsZeitschrift für angewandte Mathematik und Physik
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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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