We consider a nonlinear nonhomogeneous Robin problem with a parametric potential term and a Carathéodory reaction which is only locally defined. We show that for all values of the parameter in an ...upper half line, the equation has at least three nontrivial smooth solutions, two of constant sign and the third nodal. Under a symmetry condition on the reaction, we show the existence of a sequence of nodal solutions converging to zero in C1(Ω¯).
We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at +∞ and sublinear at −∞. 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.
In this paper, we provide both a preservation and breaking of symmetry theorem for 2π-periodic problems of the form −u′′(t)+g(u(t))=f(t)u(0)−u(2π)=u′(0)−u′(2π)=0where g:R→R is a given C1 function and ...f:0,2π→R is continuous. We provide a preservation of symmetry result that is analogous to one given by (Willem, 1989) and a generalization of the theorem given by (Costa and Fang, 2019). Both of these theorems consider the group action of translation — which corresponds to periodicity.
Abstract
We consider nonlinear Neumann problems driven by a nonhomogeneous differential operator and an indefinite potential. In this paper we are concerned with two distinct cases. We first consider ...the case where the reaction is (
p
-1)-sublinear near ±∞ and (
p
-1)-superlinear near zero. In this setting the energy functional of the problem is coercive. In the second case, the reaction is (
p
-1)-superlinear near ±∞ (without satisfying the Ambrosetti–Rabinowitz condition) and has a (
p
-1)-sublinear growth near zero. Now, the energy functional is indefinite. For both cases we prove “three solutions theorems” and in the coercive setting we provide sign information for all of them. Our approach combines variational methods, truncation and perturbation techniques, and Morse theory (critical groups).
We consider semilinear Robin problems driven by the negative Laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the Ambrosetti–Rabinowitz condition. We ...prove existence and multiplicity theorems (producing also an infinity of smooth solutions) using variational tools, truncation and perturbation techniques and Morse theory (critical groups).
In this article, we study the existence and multiplicity of solutions of the boundary-value problem $$\displaylines{ -\Delta u = f(x,u), \quad \text{in } \Omega, \cr u = 0, \quad \text{on } ...\partial\Omega, }$$ where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain with smooth boundary, $\partial\Omega$, in $\mathbb{R}^N$ $(N\geq 3)$, and f is a continuous function having subcritical growth in the second variable.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
We consider a Dirichlet nonlinear equation driven by the (
p
, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. ...We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.
PDF
