1,721,572 research outputs found
Multiple solutions for nonlinear periodic systems with combined nonlinearities and a nonsmooth potential
No full textWe consider nonlinear periodic systems driven by the p-Laplacian
and with a nonsmooth locally Lipschitz potential function. In the
right hand side forcing term, we have the combined effects of
p-sublinear (concave) and p-superlinear (convex) terms. However,
the p-superlinear term need not satisfy the Ambrosetti-Rabinowitz
condition. By combining nonsmooth critical point theory with the
Ekeland variational principle, we show that the system has at
least two nontrivial periodic solutions
Hammerstein integral inclusions in reflexive Banach spaces
No full textIn this paper we examine multivalued Hammerstein integral equations defined in a separable reflexive Banach space.We prove existence theorems for both the ‘convex’ problem (the
multifunction is convex-valued) and the ‘nonconvex’ problem (the multifunction is not necessarily convex-valued). We also show that the solution set of the latter is dense in the solution set of the former (relaxation theorem). Finally, we present some examples illustrating the applicability of
our abstract results
Nonlinear resonant periodic problems
No full textWe consider nonlinear periodic problems driven by the sum of a scalar p-Laplacian and a scalar Laplacian and a Caratheodory reaction, which at ±∞, is resonant with respect to any higher eigenvalue. Using variational methods, coupled with suitable perturbation and truncation techniques and Morse theory, we prove a three solutions theorem. For equations resonant with respect to the principal eigenvalue λ^0=0, we establish the existence of nodal solutions
Existence and multiplicity results for nonlinear eigenvalues problems with discontinuities
No full text
On p-logistic equations of equidiffusive type
No full textWe consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter varies. In the case of a unique positive solution , we investigate the monotonicity and continuity properties of the map
Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries
No full textWe consider a semilinear Dirichlet problem with an unbounded and indefinite potential and a superlinear reaction which need not satisfy the usual in such cases Ambrosetti-Rabinowitz condition. Using a combination of variational methods (critical point theory) with truncation and comparison techniques, with Morse theory and with flow invariance arguments, we show that the problems has at least seven nontrivial smooth solutions and provide sign information for all of them
Existence of two solutions for quasilinear periodic differential equations with discontinuities
Full text linksummary:In this paper we examine a quasilinear periodic problem driven by the one- dimensional -Laplacian and with discontinuous forcing term . By filling in the gaps at the discontinuity points of we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions, one positive, the other negative
On the existence of three nontrivial solutions for periodic problems driven by the scalar p-Laplacian
No full textWe consider a nonlinear periodic problem driven by the scalar
p-Laplacian with a nonsmooth potential function. First we establish
an alternative minimax expression for the first nonzero eigenvalue
for the negative periodic scalar p-Laplacian and then using it we
prove the existence of three nontrivial solutions, two of which have
constant sign. Our approach is variational based on the nonsmooth
critical point theory
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