Constant sign and nodal solutions for superlinear double phase problems

By Leszek Gasinski, Nikolaos S. Papageorgiou. Advances in Calculus of Variations, 2019

101 citations recorded by the source corpus.

Abstract We consider a double phase problems with unbalanced growth and a superlinear reaction, which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools and the Nehari method, we show that the Dirichlet problem has at least three nontrivial solutions, a positive solution, a negative solution and a nodal solution. The nodal solution has exactly two nodal domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6cdfd8bf2aa374f273078132f4d7294950815b5d

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In Applied Mathematics

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Citations in the corpus

An existence result for singular Finsler double phase problems (2020, background): “s for double phase problems in the case if F is the Euclidean norm and without singular term can be found, for example, in the papers of Colasuonno-Squassina [11], Liu-Dai [30], Gasin´ski-Papageorgiou[24], Gasin´ski-Winkert [25, 26, 27], Perera-Squassina[41] and the references therein. So far, it is”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “By the existence property of the Brouwer degree (see, for example, Gasiński-Papageorgiou [18, Theorem 4.11] or Papageorgiou-Winkert [39, Theorem 6.2.22]), we get H1(s, t) = 0 for some (s, t) ∈ D.”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “We refer to the papers of BahrouniRădulescu-Winkert [3] (Baouendi-Grushin operator), Colasuonno-Squassina [15] (double phase eigenvalue problems), Farkas-Winkert [31] (Finsler double phase problems), Gasiński-Papageorgiou [32] (locally Lipschitz right-hand sides), Gasiński-Winkert [34, 35] (convecti”
Constant sign solutions for double phase problems with superlinear nonlinearity (2019, background): “Moreover, the application of the Nehari manifold method does not seem to work for our problem because of the sign of the nonlinearity f , compare with the assumption in GasińskiPapageorgiou [9] and Liu-Dai [13].”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “Multiplicity results including sign-changing solutions have been obtained by Gasiński-Papageorgiou [37], Liu-Dai [48] and Gasiński-Winkert [40] via the Nehari manifold treatment due to the lack of regularity results for such problems.”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, background): “Finally, existence results for double phase problems with homogeneous Dirichlet or nonlinear Neumann boundary conditions without singular term can be found in the papers of Colasuonno–Squassina [13], El Manouni–Marino–Winkert [22], Gasiński–Papageorgiou [26], Gasiński–Winkert [28–30], Liu–Dai [34–”