Search results for "Asymmetric reaction"

showing 2 items of 2 documents

Four solutions for fractional p-Laplacian equations with asymmetric reactions

2020

We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.

Sublinear functionGeneral MathematicsMathematical analysisDegenerate energy levelsType (model theory)Fractional p-LaplacianCritical point (mathematics)Dirichlet distributionNonlinear systemsymbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi Matematicacritical point theory35A15 35R11 58E05p-LaplaciansymbolsFOS: Mathematicsasymmetric reactionsMathematicsMorse theoryAnalysis of PDEs (math.AP)
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Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$

2016

We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.

Variational methodsNonlinear maximum principleResonanceAsymmetric reactionCritical groupNonlinear regularity
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