Search results for " nodal solutions"
showing 6 items of 6 documents
Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero
2019
Abstract We consider parametric Dirichlet problems driven by the sum of a Laplacian and a nonhomogeneous differential operator ( ( a , 2 ) -type equation) and with a reaction term which exhibits arbitrary polynomial growth and a nonlinear dependence on the parameter. We prove the existence of three distinct nontrivial smooth solutions for small values of the parameter, providing sign information for them: one is positive, one is negative and the third one is nodal.
Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations
2021
We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.
Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations
2005
We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.
A multiplicity theorem for parametric superlinear (p,q)-equations
2020
We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
On Noncoercive (p, q)-Equations
2021
We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p - 1)-linear near +/-infinity and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.