Solitons in Several Space Dimensions:¶Derrick's Problem and¶Infinitely Many Solutions

Benci, Vieri; d’Avenia, Pietro; Fortunato, Donato; Pisani, Lorenzo

doi:10.1007/s002050000101

Cited by 210 publications

(164 citation statements)

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“…Equations driven by a (p, q)-differential operator arise in mathematical physics such as quantum physics (for existence of soliton solutions, see Benci-D'Avenia-FortunatoPisani [6]) and in plasma physics and biophysics (see Cherfils-Il yasov [11]). Recently, there have been some existence and multiplicity results for such operators.…”

Section: Mathematical Background and Hypothesesmentioning

confidence: 99%

On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Papageorgiou

Winkert

2014

Advanced Nonlinear Studies

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Abstract. We study a nonlinear parametric elliptic equation (nonlinear eigenvalue problem) driven by a nonhomogeneous differential operator. Our setting incorporates equations driven by the p-Laplacian, the (p, q)-Laplacian, and the generalized p-mean curvature differential operator. Applying variational methods we show that for λ > 0 (the parameter) sufficiently large the problem has at least three nontrivial smooth solutions whereby one is positive, one is negative and the last one has changing sign (nodal). In the particular case of (p, 2)-equations, using Morse theory, we produce another nodal solution for a total of four nontrivial smooth solutions.

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Section: Mathematical Background and Hypothesesmentioning

confidence: 99%

On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Papageorgiou

Winkert

2014

Advanced Nonlinear Studies

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“…The common feature of these papers is the superlinear and subcritical growth at infinity of the nonlinear term f . Theorem 2.1 complements several results mentioned above; we treat the case p > N which is also important from the Mathematical Physics point of view (see [6], [10]), while the nonlinear term f is allowed to have an unusual behavior. Note that closely related hypotheses to (f 1 ) and (f 2 ) have been used in [19], [20] studying boundary value problems.…”

Section: Statement Of the Main Resultsmentioning

confidence: 70%

Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in $${\mathbb{R}}^N$$

Kristály

Marzantowicz

2008

Nonlinear differ. equ. appl.

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“…We mention that equations involving the sum of a p-Laplacian and a Laplacian (also known as ( p, 2)-equations) arise in mathematical physics; see, for example, the works of Benci et al [13] (quantum physics) and Cherfils and Il yasov [14] (plasma physics).…”

Section: ( )mentioning

confidence: 99%

Resonant (p, 2)-equations with concave terms

Papageorgiou

Winkert

2014

Applicable Analysis

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We consider a nonlinear, nonhomogeneous parametric elliptic Dirichlet equation driven by the sum of a p-Laplacian and a Laplacian (so-called (p,2)-equation) and with a nonlinearity involving a concave term which enters with a negative sign. By applying variational methods along with truncation and comparison techniques as well as Morse theory (critical groups), we show that the problem under consideration has at least five nontrivial solutions (four of them have constant sign) for all sufficiently small values of the parameter.

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Solitons in Several Space Dimensions:¶Derrick's Problem and¶Infinitely Many Solutions

Cited by 210 publications

References 10 publications

On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in $${\mathbb{R}}^N$$

Resonant (p, 2)-equations with concave terms

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