Abstract
In this article, using a fixed point index theorem on a cone, we prove the existence and multiplicity results of positive solutions to a one-dimensional p-Laplacian problem defined on infinite intervals. We also establish the nonexistence results of nontrivial solutions to the problem.
Highlights
We are concerned with the following one-dimensional p-Laplacian problem defined on infinite intervals:
Where 1 < p < N, φ p (s) := |s| p−2 s for s ∈ R \ {0}, φ p (0) := 0, K ∈ C1 (R+, R+ ) with R+ = (0, ∞), f is an odd and locally Lipschitz-continuous function on R, and R is a positive parameter
Let v be a nontrivial solution to Problem (5)
Summary
On the contrary, that there exists a nontrivial solution u to Problem (1). By ( F3), R [K (r )] p dr → 0 as R → ∞, and there exists R∗ > 0 such that Problem (1) has no nontrivial solution for any R > R∗ .
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