We consider a parametric (p,q)-equations with sign-changing reaction and Robin boundary condition. We show that for all values of the parameter λ bigger than a certain value which we determine ...precisely, the problem has at least three nontrivial solutions all with sign information and ordered. For the particular case of (p,2)-equations we produce a second nodal solution, for a total of four nontrivial solutions. Under symmetry conditions, we show the existence of infinitely many nodal solutions. The same results are also valid for the Dirichlet problem.
We consider a nonlinear eigenvalue problem for the Dirichlet (p,q)$(p,q)$‐Laplacian with a sign‐changing Carathé$\acute{\rm e}$odory reaction. Using variational tools, truncation and comparison ...techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter λ>0$\lambda >0$ (bifurcation‐type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).
We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct ...nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.
We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, ...critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered.
For more information see https://ejde.math.txstate.edu/Volumes/2021/12/abstr.html
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this paper we study the existence and multiplicity of solutions of the boundary–value problem(1){−Δu=−λ|u|q−2u+au+b(u+)p−1, in Ω;u=0, on ∂Ω, where Δ denotes the N-dimensional Laplacian, Ω is a ...bounded domain with smooth boundary, ∂Ω, in RN(N⩾3), u+ denotes the positive part of u:Ω→R, 1<q<2<p<2⁎=2N/(N−2), λ>0, a∈R and b>0. Using infinite-dimensional Morse Theory, we extend the results of Paiva and Presoto 14 and establish some conditions for the existence of at least four nontrivial solutions of (1).
We consider a semilinear Dirichlet problem with a reaction which exhibits an asymmetric behaviour as
$ x \to \pm \infty $
x
→
±
∞
(it is superlinear as
$ x \to +\infty $
x
→
+
∞
and resonant as
$ x ...\to -\infty $
x
→
−
∞
). Using variational tools from the critical point theory, together with truncation and comparison techniques and critical groups, we prove two multiplicity theorems producing two and three nontrivial solutions. Also we show that the problem can not have negative solutions.
We study a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian (2<p<+∞) and a jumping nonlinearity. Under very general conditions on the reaction and without ...using the Fučik spectrum, we show that the problem has at least three nontrivial solutions and we provide sign information for all of them. Our approach uses critical point theory, truncation and comparison techniques and Morse theory.
We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a ...negative sign and of an asymmetric asymptotically linear term which is resonant in the negative direction. Using variational methods together with truncation and perturbation techniques and Morse theory (critical groups), we prove two multiplicity theorems producing four and five, respectively, nontrivial smooth solutions when the parameter
is small.
In this note we present a symmetry breaking result for a class of 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. Our approach is inspired on Willem’s paper (Willem, 1989) and uses actions of finite groups which are not usually considered in the literature.
PDF
