2013
DOI: 10.1186/1687-2770-2013-86
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Nontrivial solutions of Hammerstein integral equations with reflections

Abstract: Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first-order periodic boundary value problem with reflections. MSC: Primary 34K10; secondary 34B15; 34K13

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Cited by 20 publications
(34 citation statements)
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“…Remark 2.11. We point out that, on the contrary to function G and ∂ G ∂ t , it is not possible to find a continuous functiong 2 …”
Section: Lemma 24 ([13 Lemma 4])mentioning
confidence: 92%
See 2 more Smart Citations
“…Remark 2.11. We point out that, on the contrary to function G and ∂ G ∂ t , it is not possible to find a continuous functiong 2 …”
Section: Lemma 24 ([13 Lemma 4])mentioning
confidence: 92%
“…To do that, we will use the fixed point index theory. Similar arguments have been applied in [2] to functional equations that only depend on the values of the solution u. First of all, we will compile some classical results regarding to this theory (see [1,7] for more details).…”
Section: Existence and Multiplicity Of Solutionsmentioning
confidence: 99%
See 1 more Smart Citation
“…On the other hand, we obtain the following values for the limits over the nonlinearity f : Therefore, from Corollary 4, we deduce that for all λ ∈ (4, ∞), T has at least a fixed point in the cone K, with independence of the choice of t 1 . This fixed point is a nontrivial solution of problem (4).…”
Section: Moreover It Is Obvious Thatmentioning
confidence: 98%
“…In this section we will use the fixed point index theory to study the existence of multiple fixed points of operator T . In [4] the authors apply similar arguments to functional equations that only depend on the values of u. First of all, we compile some classical results regarding to fixed point index (see [2,11] for the details).…”
Section: Existence and Multiplicity Of Solutionsmentioning
confidence: 99%