Bifurcation for indefinite‐weighted p$p$ ‐Laplacian problems with slightly subcritical nonlinearity
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DOI: 10.1002/mana.202400184
Abstract: We study a superlinear elliptic boundary value problem involving the p$p$ ‐Laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the… read more here.
Keywords: indefinite weighted; weighted laplacian; laplacian problems; problems slightly ... See more keywords
Neumann p-Laplacian problems with a reaction term on metric spaces
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DOI: 10.1007/s11587-020-00532-6
Abstract: We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincare inequality. Trace… read more here.
Keywords: neumann laplacian; metric spaces; reaction term; term metric ... See more keywords
Positive solutions for semipositone (p,N)-Laplacian problems with critical Trudinger–Moser nonlinearities
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DOI: 10.1007/s13163-021-00386-y
Abstract: In this paper, we deal with the existence of positive solutions for semipositone (p,N)-Laplacian problems with critical Trudinger–Moser nonlinearities in a bounded domain: $$\begin{aligned} \left\{ \begin{array}{clll} -\varDelta _p u-\varDelta _N u=\lambda u^{N-1}e^{\beta u^{N'}} - \mu… read more here.
Keywords: critical trudinger; semipositone laplacian; solutions semipositone; positive solutions ... See more keywords
A uniqueness result for infinite semipositone p-Laplacian problems in a ball
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DOI: 10.1080/17476933.2021.1882437
Abstract: We prove the uniqueness of positive radial solutions to a class of singular p-Laplacian equations in a ball with Dirichlet boundary condition when a parameter is large. The reaction term exhibits i... read more here.
Keywords: semipositone laplacian; infinite semipositone; problems ball; laplacian problems ... See more keywords
Existence of Positive Solutions for a System of Generalized Laplacian Problems
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DOI: 10.3390/math13203322
Abstract: This paper investigates the existence and multiplicity of positive solutions for a system of generalized Laplacian problems. By analyzing the asymptotic behavior of nonlinearity, we establish conditions for the existence of positive solutions and the… read more here.
Keywords: solutions system; positive solutions; laplacian problems; system generalized ... See more keywords
Infinitely Many Solutions for the Fractional p&q-Laplacian Problems in RN
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DOI: 10.3390/sym14122486
Abstract: In this paper, we consider the following class of the fractional p&q-Laplacian problem: (−Δ)psu+(−Δ)qsu+V(x)(|u|p−2u+|u|q−2u)+g(x)|u|r−2u=K(x)f(x,u)+h(u),x∈RN,V:RN→R+ is a potential function, and h:R→R is a perturbation term. We studied two cases: if f(x,u) is sublinear, by means of… read more here.
Keywords: solutions fractional; fractional laplacian; many solutions; laplacian problems ... See more keywords
Uniqueness for a class p-Laplacian problems when a parameter is large
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DOI: 10.7494/opmath.2024.44.1.5
Abstract: We prove uniqueness of positive solutions for the problem \[-\Delta_{p}u=\lambda f(u)\text{ in }\Omega,\ u=0\text{ on }\partial \Omega,\] where \(1\lt p\lt 2\) and \(p\) is close to 2, \(\Omega\) is bounded domain in \(\mathbb{R}^{n}\) with smooth… read more here.
Keywords: parameter large; problems parameter; laplacian problems; class laplacian ... See more keywords